What is the solution for (d^2y)/(dx^2)-(dy)/(dx)+6x=0 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)+6x=0 is y=c_{1}e^x+c_{2}+3x^2+6x

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(d^2y)/(dx^2)-(dy)/(dx)+6x=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 6 x = 0

y = c_{1} e^{x} + c_{2} + 3 x^{2} + 6 x

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 6 x = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} + 3 x^{2} + 6 x

y = c_{1} e^{x} + c_{2} + 3 x^{2} + 6 x

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

2 y^{^{''}} + y^{^{'}} - y = 1, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3} x

2 y^{^{''}} - y^{^{'}} - y = 3 e^{x} + 2 e^{- x}

y^{^{''}} + 2 y^{^{'}} + y = t^{(- 1)} e^{(- t)}

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)+6x=0 ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)+6x=0 is y=c_{1}e^x+c_{2}+3x^2+6x