Question

Is there a way to solve following ODE?
I will put the equation in reply!

Answer 1

\[\frac{ dU _{c} }{ dt }+Dw ^{2}U _{c}=-\sqrt{\frac{ 2 }{ \pi }}D\left\{ \frac{ 1 }{ a }g(t) -h(x,t) \right\}\]
By Integrating factor I got answer as
\[U _{c}=-\frac{D}{a} \sqrt{\frac{ 2 }{ \pi }}\int\limits\limits_{0}^{t}g(\tau)-h(x,\tau)\exp(-Dw ^{2}(t-\tau)d \tau \]
But problem is Uc is transferred form of h(x, tau) and we have to transform it back to h(x,t) , which is what we want to find out. So I need solution of given ODE such that h(x, tau) remains outside integral so that it can be taken other side of equation.