1.

What is the solution of, \(\frac{∂^2 u}{∂x^2}=2xe^t,\) after applying method of separation of variables \((u(0,t)=t,\frac{∂u}{∂x} (0,t)= e^t)\)?

A. \(u=\frac{x^3}{3} e^t+xe^t \)
B. \(u=\frac{x^3}{3} e^t+xe^t+t\)
C. \(u=\frac{x^3}{3} e^t+e^t+t\)
D. \(u=\frac{x^2}{2} e^t+xe^t+t\)
Answer» C. \(u=\frac{x^3}{3} e^t+e^t+t\)


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