How to solve the following relation related to Laplace transformation?

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I tried solving it by integrating by parts but i was unsuccessful.enter image description here






differential-equations laplace-transform







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  • 3




    Start from the right hand side.
    – Nosrati
    1 hour ago










  • @Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
    – RockDock
    1 hour ago







  • 2




    by changing variables.
    – Nosrati
    1 hour ago














up vote
3
down vote

favorite
1












I tried solving it by integrating by parts but i was unsuccessful.enter image description here






differential-equations laplace-transform







share|cite|improve this question

















  • 3




    Start from the right hand side.
    – Nosrati
    1 hour ago










  • @Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
    – RockDock
    1 hour ago







  • 2




    by changing variables.
    – Nosrati
    1 hour ago












up vote
3
down vote

favorite
1









up vote
3
down vote

favorite
1






1





I tried solving it by integrating by parts but i was unsuccessful.enter image description here






differential-equations laplace-transform







share|cite|improve this question













I tried solving it by integrating by parts but i was unsuccessful.enter image description here






differential-equations laplace-transform




differential-equations laplace-transform






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 1 hour ago









RockDock

483




483







  • 3




    Start from the right hand side.
    – Nosrati
    1 hour ago










  • @Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
    – RockDock
    1 hour ago







  • 2




    by changing variables.
    – Nosrati
    1 hour ago












  • 3




    Start from the right hand side.
    – Nosrati
    1 hour ago










  • @Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
    – RockDock
    1 hour ago







  • 2




    by changing variables.
    – Nosrati
    1 hour ago







3




3




Start from the right hand side.
– Nosrati
1 hour ago




Start from the right hand side.
– Nosrati
1 hour ago












@Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
– RockDock
1 hour ago





@Nosrati i am getting two integrals multiplied together.how to bring them in single one ?
– RockDock
1 hour ago





2




2




by changing variables.
– Nosrati
1 hour ago




by changing variables.
– Nosrati
1 hour ago










1 Answer
1






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up vote
4
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accepted










beginalign
F(p) G(p)
&= int_0^infty e^-puf(u) duint_0^infty e^-pvg(v) dv \
&= int_0^inftyint_0^infty e^-p(u+v)f(u)g(v) du dv ,,, , ,,, textu+v=t ,, , ,, textv=x\
&= int_0^inftyint_x^infty e^-ptf(t-x)g(x) dt dx \
&= int_0^infty e^-ptBig[int_0^xf(t-x)g(x) dx Big] dt \
&= cal L(f*g)(t)
endalign






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  • 1




    I think you might be right, let me correct another time, thank you.
    – Nosrati
    5 mins ago










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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
4
down vote



accepted










beginalign
F(p) G(p)
&= int_0^infty e^-puf(u) duint_0^infty e^-pvg(v) dv \
&= int_0^inftyint_0^infty e^-p(u+v)f(u)g(v) du dv ,,, , ,,, textu+v=t ,, , ,, textv=x\
&= int_0^inftyint_x^infty e^-ptf(t-x)g(x) dt dx \
&= int_0^infty e^-ptBig[int_0^xf(t-x)g(x) dx Big] dt \
&= cal L(f*g)(t)
endalign






share|cite|improve this answer
















  • 1




    I think you might be right, let me correct another time, thank you.
    – Nosrati
    5 mins ago














up vote
4
down vote



accepted










beginalign
F(p) G(p)
&= int_0^infty e^-puf(u) duint_0^infty e^-pvg(v) dv \
&= int_0^inftyint_0^infty e^-p(u+v)f(u)g(v) du dv ,,, , ,,, textu+v=t ,, , ,, textv=x\
&= int_0^inftyint_x^infty e^-ptf(t-x)g(x) dt dx \
&= int_0^infty e^-ptBig[int_0^xf(t-x)g(x) dx Big] dt \
&= cal L(f*g)(t)
endalign






share|cite|improve this answer
















  • 1




    I think you might be right, let me correct another time, thank you.
    – Nosrati
    5 mins ago












up vote
4
down vote



accepted







up vote
4
down vote



accepted






beginalign
F(p) G(p)
&= int_0^infty e^-puf(u) duint_0^infty e^-pvg(v) dv \
&= int_0^inftyint_0^infty e^-p(u+v)f(u)g(v) du dv ,,, , ,,, textu+v=t ,, , ,, textv=x\
&= int_0^inftyint_x^infty e^-ptf(t-x)g(x) dt dx \
&= int_0^infty e^-ptBig[int_0^xf(t-x)g(x) dx Big] dt \
&= cal L(f*g)(t)
endalign






share|cite|improve this answer












beginalign
F(p) G(p)
&= int_0^infty e^-puf(u) duint_0^infty e^-pvg(v) dv \
&= int_0^inftyint_0^infty e^-p(u+v)f(u)g(v) du dv ,,, , ,,, textu+v=t ,, , ,, textv=x\
&= int_0^inftyint_x^infty e^-ptf(t-x)g(x) dt dx \
&= int_0^infty e^-ptBig[int_0^xf(t-x)g(x) dx Big] dt \
&= cal L(f*g)(t)
endalign







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 1 hour ago









Nosrati

25k62052




25k62052







  • 1




    I think you might be right, let me correct another time, thank you.
    – Nosrati
    5 mins ago












  • 1




    I think you might be right, let me correct another time, thank you.
    – Nosrati
    5 mins ago







1




1




I think you might be right, let me correct another time, thank you.
– Nosrati
5 mins ago




I think you might be right, let me correct another time, thank you.
– Nosrati
5 mins ago

















 

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