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

Use Laplace transform to solve the following initial value problem:
${y}^{″}+5y=1+t,y\left(0\right)=0,{y}^{\prime }\left(0\right)=4$
A)$\frac{7}{25}{e}^{t}\mathrm{cos}\left(2t\right)+\frac{21}{10}{e}^{t}\mathrm{sin}\left(2t\right)$
B) $\frac{7}{2}+\frac{t}{5}-\frac{t}{25}{e}^{t}\mathrm{cos}\left(2t\right)+\frac{21}{10}{e}^{t}\mathrm{sin}\left(2t\right)$
C) $\frac{7}{25}+\frac{t}{5}$
D) $\frac{7}{25}+\frac{t}{5}-\frac{7}{25}{e}^{t}\mathrm{cos}\left(2t\right)+\frac{21}{10}{e}^{t}\mathrm{sin}\left(2t\right)$
E) non of the above
F) $\frac{7}{25}+\frac{t}{5}-\frac{7}{5}{e}^{t}\mathrm{cos}\left(2t\right)+\frac{21}{10}{e}^{t}\mathrm{sin}\left(2t\right)$

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