What is the solution for 3x(dy)/(dx)+9x^3y=3x^3 ?

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

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3x(dy)/(dx)+9x^3y=3x^3

3 x \frac{d y}{d x} + 9 x^{3} y = 3 x^{3}

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

Solution steps

3 x \frac{d y}{d x} + 9 x^{3} y = 3 x^{3}

Solve separable ODE:

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

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

x \frac{d y}{d x} + cot (y) = 0

N^{^{'}} = r - a (N - b)^{2}

y^{^{'}} = \frac{1}{2} y cos^{2} (y)

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

\frac{d h}{d t} = - \frac{3}{100} h - 19

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