What is the solution for (dy)/(dx)=x^2(-6y+9) ?

The solution for (dy)/(dx)=x^2(-6y+9) is y=(e^{-2x^3-c_{1}})/2+3/2

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(dy)/(dx)=x^2(-6y+9)

\frac{d y}{d x} = x^{2} (- 6 y + 9)

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

Solution steps

\frac{d y}{d x} = x^{2} (- 6 y + 9)

Solve separable ODE:

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

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

What is the solution for (dy)/(dx)=x^2(-6y+9) ?
The solution for (dy)/(dx)=x^2(-6y+9) is y=(e^{-2x^3-c_{1}})/2+3/2