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How to obtain the solution of an ODE in implicit form?
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I want to get the general solution of a first-order ODE in implicit form.
It should be something like this:
- With input
y'[x] == 1, the desired output isC[1]->y[x] - x. - With input
y'[x] == 1/y[x]^2(nonlinear ODE), the desired output isC[1]->y[x]^3/3 - x
DSolve tries to evaluate the explicit form of y[x] by default. Is it possible to keep the implicit solution?
I tried explicit equation integration using Integrate and tracing (Trace with TraceInternal -> True). Neither helped me with this problem.
differential-equations
edited 24 mins ago
m_goldberg
82.8k870191
asked 2 hours ago
Ilya
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up vote
1
down vote
favorite
I want to get the general solution of a first-order ODE in implicit form.
It should be something like this:
- With input
y'[x] == 1, the desired output isC[1]->y[x] - x. - With input
y'[x] == 1/y[x]^2(nonlinear ODE), the desired output isC[1]->y[x]^3/3 - x
DSolve tries to evaluate the explicit form of y[x] by default. Is it possible to keep the implicit solution?
I tried explicit equation integration using Integrate and tracing (Trace with TraceInternal -> True). Neither helped me with this problem.
differential-equations
edited 24 mins ago
m_goldberg
82.8k870191
asked 2 hours ago
Ilya
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
But this seems not to work correctly.Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqnreturns-1 + y[x] == 0with no integration constant
– Ilya
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I want to get the general solution of a first-order ODE in implicit form.
It should be something like this:
- With input
y'[x] == 1, the desired output isC[1]->y[x] - x. - With input
y'[x] == 1/y[x]^2(nonlinear ODE), the desired output isC[1]->y[x]^3/3 - x
DSolve tries to evaluate the explicit form of y[x] by default. Is it possible to keep the implicit solution?
I tried explicit equation integration using Integrate and tracing (Trace with TraceInternal -> True). Neither helped me with this problem.
differential-equations
edited 24 mins ago
m_goldberg
82.8k870191
asked 2 hours ago
Ilya
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I want to get the general solution of a first-order ODE in implicit form.
It should be something like this:
- With input
y'[x] == 1, the desired output isC[1]->y[x] - x. - With input
y'[x] == 1/y[x]^2(nonlinear ODE), the desired output isC[1]->y[x]^3/3 - x
DSolve tries to evaluate the explicit form of y[x] by default. Is it possible to keep the implicit solution?
I tried explicit equation integration using Integrate and tracing (Trace with TraceInternal -> True). Neither helped me with this problem.
differential-equations
differential-equations
edited 24 mins ago
m_goldberg
82.8k870191
asked 2 hours ago
Ilya
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 24 mins ago
m_goldberg
82.8k870191
asked 2 hours ago
Ilya
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 24 mins ago
m_goldberg
82.8k870191
edited 24 mins ago
m_goldberg
82.8k870191
edited 24 mins ago
m_goldberg
82.8k870191
82.8k870191
asked 2 hours ago
Ilya
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Ilya
62
asked 2 hours ago
Ilya
62
62
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ilya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
But this seems not to work correctly.Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqnreturns-1 + y[x] == 0with no integration constant
– Ilya
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago
add a comment |Â
1
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
But this seems not to work correctly.Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqnreturns-1 + y[x] == 0with no integration constant
– Ilya
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago
1
1
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
But this seems not to work correctly.
Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqn returns -1 + y[x] == 0 with no integration constant– Ilya
2 hours ago
But this seems not to work correctly.
Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqn returns -1 + y[x] == 0 with no integration constant– Ilya
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago
add a comment |Â
1 Answer
1
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votes
up vote
2
down vote
The following works for the two examples in the OP:
eq = y'[x] == 1; (* try also eq = y'[x] == 1/y[x]^2 *)
Solve[Equal @@ DSolve[eq, y[x], x][[1, 1]], C[1]]
(* C[1] -> -x + y[x] *)
Higher order ODEs contain more constants of integration, so OP shall modify the code accordingly.
answered 1 hour ago
AccidentalFourierTransform
4,6021839
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
The following works for the two examples in the OP:
eq = y'[x] == 1; (* try also eq = y'[x] == 1/y[x]^2 *)
Solve[Equal @@ DSolve[eq, y[x], x][[1, 1]], C[1]]
(* C[1] -> -x + y[x] *)
Higher order ODEs contain more constants of integration, so OP shall modify the code accordingly.
answered 1 hour ago
AccidentalFourierTransform
4,6021839
add a comment |Â
up vote
2
down vote
The following works for the two examples in the OP:
eq = y'[x] == 1; (* try also eq = y'[x] == 1/y[x]^2 *)
Solve[Equal @@ DSolve[eq, y[x], x][[1, 1]], C[1]]
(* C[1] -> -x + y[x] *)
Higher order ODEs contain more constants of integration, so OP shall modify the code accordingly.
answered 1 hour ago
AccidentalFourierTransform
4,6021839
add a comment |Â
up vote
2
down vote
up vote
2
down vote
The following works for the two examples in the OP:
eq = y'[x] == 1; (* try also eq = y'[x] == 1/y[x]^2 *)
Solve[Equal @@ DSolve[eq, y[x], x][[1, 1]], C[1]]
(* C[1] -> -x + y[x] *)
Higher order ODEs contain more constants of integration, so OP shall modify the code accordingly.
answered 1 hour ago
AccidentalFourierTransform
4,6021839
The following works for the two examples in the OP:
eq = y'[x] == 1; (* try also eq = y'[x] == 1/y[x]^2 *)
Solve[Equal @@ DSolve[eq, y[x], x][[1, 1]], C[1]]
(* C[1] -> -x + y[x] *)
Higher order ODEs contain more constants of integration, so OP shall modify the code accordingly.
answered 1 hour ago
AccidentalFourierTransform
4,6021839
answered 1 hour ago
AccidentalFourierTransform
4,6021839
answered 1 hour ago
AccidentalFourierTransform
4,6021839
answered 1 hour ago
AccidentalFourierTransform
4,6021839
4,6021839
add a comment |Â
add a comment |Â
Ilya is a new contributor. Be nice, and check out our Code of Conduct.
Ilya is a new contributor. Be nice, and check out our Code of Conduct.
Ilya is a new contributor. Be nice, and check out our Code of Conduct.
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1
Strongly related, if not duplicate: mathematica.stackexchange.com/q/137598/1871
– xzczd
2 hours ago
But this seems not to work correctly.
Quiet@Trace[DSolve[y'[x] == 1, y[x], x], Solve[e_, y[x]] -> (eqn = e), TraceInternal -> True]; eqnreturns-1 + y[x] == 0with no integration constant– Ilya
2 hours ago
Yes, and that's the reason I didn't vote for close as duplicate.
– xzczd
2 hours ago