Use Laplace transform to solve the following initial value problem:y"-2y'+5y=1+t , y(0)=0 , y'(0)=4

Clifland 2021-09-24 Answered

Use Laplace transform to solve the following initial value problem:
$y^{″} + 5 y = 1 + t, y (0) = 0, y^{'} (0) = 4$
A) $\frac{7}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
B) $\frac{7}{2} + \frac{t}{5} - \frac{t}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
C) $\frac{7}{25} + \frac{t}{5}$
D) $\frac{7}{25} + \frac{t}{5} - \frac{7}{25} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$
E) non of the above
F) $\frac{7}{25} + \frac{t}{5} - \frac{7}{5} e^{t} \cos (2 t) + \frac{21}{10} e^{t} \sin (2 t)$

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