What is the solution for y^{''}+y=3e^{-7x},y(0)=0,y^'(0)=0 ?

The solution for y^{''}+y=3e^{-7x},y(0)=0,y^'(0)=0 is y=-3/50 cos(x)+21/50 sin(x)+3/50 e^{-7x}

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y^{''}+y=3e^{-7x},y(0)=0,y^'(0)=0

y^{^{''}} + y = 3 e^{- 7 x}, y (0) = 0, y^{^{'}} (0) = 0

y = - \frac{3}{50} cos (x) + \frac{21}{50} sin (x) + \frac{3}{50} e^{- 7 x}

Solution steps

y^{''} (x) + y = 3 e^{- 7 x}

Solve linear ODE:

y = - \frac{3}{50} cos (x) + \frac{21}{50} sin (x) + \frac{3}{50} e^{- 7 x}

y = - \frac{3}{50} cos (x) + \frac{21}{50} sin (x) + \frac{3}{50} e^{- 7 x}

y^{^{''}} + 4 y = e^{2 x}

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

y^{^{''}} - 9 y^{^{'}} + 14 y = 3 x^{2} - 5 sin (2 x) + 8 x e^{6 x}

2 y^{^{''}} + 4 y^{^{'}} + 2 y = \frac{1}{e ^{x} ( x + 1 )}

y^{^{''}} + y = x + 1

What is the solution for y^{''}+y=3e^{-7x},y(0)=0,y^'(0)=0 ?
The solution for y^{''}+y=3e^{-7x},y(0)=0,y^'(0)=0 is y=-3/50 cos(x)+21/50 sin(x)+3/50 e^{-7x}