Mathematical Methods in the Physical Sciences · Problem 5.17

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · convolution-differential-equations

Problem

Solve the differential equation y′′−a2y=f(t)y'' - a^2 y = f(t), where f(t)={0,t<0,1,t>0,andy0=y0′=0.f(t) = \begin{cases} 0, & t < 0, \\ 1, & t > 0, \end{cases} \quad \text{and} \quad y_0 = y_0' = 0. Hint: Use the convolution integral as in the example.

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