MAT244-2013F > Quiz 2

Problem 2, night sections


Victor Ivrii:
Find the general solution of the given differential equation:
y''-y'-2y = -2t + 4t^2.

Yangming Cai:
answers as follow

Ka Hou Cheok:
Let the solution $y=y_c+Y$,

The characteristic equation for the homogeneous equation $y''-y'-2y=0$ is
Solving the equation we have $r_1=2, r_2=-1$ and hence $$y_c=C_1\exp(2t)+C_2\exp(-t)$$

Let $Y=At^2+Bt+C$, $Y'=2tA+B$, $Y''=2A$.


By comparing the coefficients,
So, $Y=-2t^2+3t-\frac{7}{2}$ and hence $$y=y_c+Y=C_1\exp(2t)+C_2\exp(-t)-2t^2+3t-\frac{7}{2}$$

Tianqi Chen:


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