What is the solution for y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7 ?

The solution for y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7 is y=(5/2+1/2)e^t-5/2 e^{-2t}-t-1/2

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y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 7

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

Solution steps

y^{''} (t) + y^{'} (t) - 2 y = 2 t

Solve linear ODE:

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

y = x^{3} - 2 x + 2 (2.6)

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\int_{0}^{\frac{π}{2}} 24 x^{2} sin (x) d x

x \to 0 - lim (\frac{3}{x ^{2} - x})

\int \frac{- x - 8}{x ^{2} + 9} d x

What is the solution for y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7 ?
The solution for y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7 is y=(5/2+1/2)e^t-5/2 e^{-2t}-t-1/2