What is the solution for y^{''}+y^'-6y=12x-50sin(x) ?

The solution for y^{''}+y^'-6y=12x-50sin(x) is y=c_{1}e^{2x}+c_{2}e^{-3x}-2x-1/3+7sin(x)+cos(x)

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y^{''}+y^'-6y=12x-50sin(x)

y^{^{''}} + y^{^{'}} - 6 y = 12 x - 50 sin (x)

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 2 x - \frac{1}{3} + 7 sin (x) + cos (x)

Solution steps

y^{''} (x) + y^{'} (x) - 6 y = 12 x - 50 sin (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 2 x - \frac{1}{3} + 7 sin (x) + cos (x)

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 2 x - \frac{1}{3} + 7 sin (x) + cos (x)

\frac{d ^{2}}{d x ^{2}} (cos (7 x))

y^{^{'}} = 3 x (y + 4)^{2}

f (t) = t - 4

\int \frac{6 x ^{2} - 5 x + 8}{x ^{3} + 4 x} d x

\int_{0}^{4} 16 x^{2} - x^{4} d x

What is the solution for y^{''}+y^'-6y=12x-50sin(x) ?
The solution for y^{''}+y^'-6y=12x-50sin(x) is y=c_{1}e^{2x}+c_{2}e^{-3x}-2x-1/3+7sin(x)+cos(x)