What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)=12x^2 ?

The solution for (d^2y)/(dx^2)+2(dy)/(dx)=12x^2 is y=c_{1}+c_{2}e^{-2x}+2x^3-3x^2+3x

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(d^2y)/(dx^2)+2(dy)/(dx)=12x^2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 12 x^{2}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 12 x^{2}

Solve linear ODE:

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

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

\int \frac{( 2 x + 11 )}{x ^{2} + x - 6} d x

\int \frac{1}{x 49 + x ^{2}} d x

f (x) = x (5 e^{x} - 4 x^{4})

\int 2^{x^{2}} d x

\frac{1}{( s ^{2} + 6 π s + π ^{2} )}

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)=12x^2 ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)=12x^2 is y=c_{1}+c_{2}e^{-2x}+2x^3-3x^2+3x