What is the solution for (dy)/(dx)+18x^2y=5x^2,y(0)=4 ?

The solution for (dy)/(dx)+18x^2y=5x^2,y(0)=4 is y=(67e^{-6x^3})/(18)+5/18

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(dy)/(dx)+18x^2y=5x^2,y(0)=4

\frac{d y}{d x} + 18 x^{2} y = 5 x^{2}, y (0) = 4

y = \frac{67 e ^{- 6 x^{3}}}{18} + \frac{5}{18}

Solution steps

\frac{d y}{d x} + 18 x^{2} y = 5 x^{2}

Solve separable ODE:

y = \frac{67 e ^{- 6 x^{3}}}{18} + \frac{5}{18}

y = \frac{67 e ^{- 6 x^{3}}}{18} + \frac{5}{18}

\frac{d x}{d t} + \frac{x}{50} = 4

x^{5} (\frac{d y}{d x}) = 3 x^{2} 1 - y^{2}

x \frac{d y}{d x} = 1 - y^{2}

\frac{d y}{d x} + 24 x^{2} y = 24 x^{2}

y^{^{'}} - y = y^{2}

What is the solution for (dy)/(dx)+18x^2y=5x^2,y(0)=4 ?
The solution for (dy)/(dx)+18x^2y=5x^2,y(0)=4 is y=(67e^{-6x^3})/(18)+5/18