By utilizing the Laplace transforms, solve the 1st-oder partial differential equation = 5x sin 2t, w(x,0)...

 

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By utilizing the Laplace transforms, solve the 1st-oder partial differential equation = 5x sin 2t, w(x,0) = 0, w(1,t) = 2e-t — 2 cos 2t + sin 2t. Əw əw X + = əx at Note that the general solution of the 1st-order linear ODE y' + p(x)y = r(x) can be obtained as y(x) = e-h[fe¹rdx+c] where h(x) = f p(x)dx. By utilizing the Laplace transforms, solve the 1st-oder partial differential equation = 5x sin 2t, w(x,0) = 0, w(1,t) = 2e-t — 2 cos 2t + sin 2t. Əw əw X + = əx at Note that the general solution of the 1st-order linear ODE y' + p(x)y = r(x) can be obtained as y(x) = e-h[fe¹rdx+c] where h(x) = f p(x)dx.

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SOLUTION To solve the given partial differential equation using Laplace transforms we need to take t... View the full answer