What is the solution for y^{''}+y=9e^{-7x},y(0)=0,y^'(0)=0 ?

The solution for y^{''}+y=9e^{-7x},y(0)=0,y^'(0)=0 is y=-9/50 cos(x)+63/50 sin(x)+9/50 e^{-7x}

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y^{''}+y=9e^{-7x},y(0)=0,y^'(0)=0

y^{^{''}} + y = 9 e^{- 7 x}, y (0) = 0, y^{^{'}} (0) = 0

y = - \frac{9}{50} cos (x) + \frac{63}{50} sin (x) + \frac{9}{50} e^{- 7 x}

Solution steps

y^{''} (x) + y = 9 e^{- 7 x}

Solve linear ODE:

y = - \frac{9}{50} cos (x) + \frac{63}{50} sin (x) + \frac{9}{50} e^{- 7 x}

y = - \frac{9}{50} cos (x) + \frac{63}{50} sin (x) + \frac{9}{50} e^{- 7 x}

y^{^{''}} + 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y^{^{''}} + 18 y^{^{'}} + 81 y = x, y (0) = 0, y^{^{'}} (0) = 0

20 y^{^{''}} + 9 y^{^{'}} + x = 0, y (0) = 0, y^{^{'}} (0) = 3

d, d (x) = \frac{2 x ^{3} + 1}{x ^{6}}

y^{^{''}} + 9 y = 18 cos (3 x)

What is the solution for y^{''}+y=9e^{-7x},y(0)=0,y^'(0)=0 ?
The solution for y^{''}+y=9e^{-7x},y(0)=0,y^'(0)=0 is y=-9/50 cos(x)+63/50 sin(x)+9/50 e^{-7x}