What is the solution for y^{''}+6y^'-7y=21x^2-8x-30 ?

The solution for y^{''}+6y^'-7y=21x^2-8x-30 is y=c_{1}e^x+c_{2}e^{-7x}-3x^2-4x

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y^{''}+6y^'-7y=21x^2-8x-30

y^{^{''}} + 6 y^{^{'}} - 7 y = 21 x^{2} - 8 x - 30

y = c_{1} e^{x} + c_{2} e^{- 7 x} - 3 x^{2} - 4 x

Solution steps

y^{''} (x) + 6 y^{'} (x) - 7 y = 21 x^{2} - 8 x - 30

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 7 x} - 3 x^{2} - 4 x

y = c_{1} e^{x} + c_{2} e^{- 7 x} - 3 x^{2} - 4 x

y^{^{''}} + y^{^{'}} - 2 y = e^{- 2 \cdot x} sin (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x + 4, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 5 y = x e^{x}

y^{^{''}} + 9 y = 5 x, y (0) = 1, y^{^{'}} (0) = 3

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

What is the solution for y^{''}+6y^'-7y=21x^2-8x-30 ?
The solution for y^{''}+6y^'-7y=21x^2-8x-30 is y=c_{1}e^x+c_{2}e^{-7x}-3x^2-4x