What is the solution for (dy)/(dx)+12x^2y=7x^2,y(0)=2 ?

The solution for (dy)/(dx)+12x^2y=7x^2,y(0)=2 is y=(17e^{-4x^3})/(12)+7/12

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(dy)/(dx)+12x^2y=7x^2,y(0)=2

\frac{d y}{d x} + 12 x^{2} y = 7 x^{2}, y (0) = 2

y = \frac{17 e ^{- 4 x^{3}}}{12} + \frac{7}{12}

Solution steps

\frac{d y}{d x} + 12 x^{2} y = 7 x^{2}

Solve separable ODE:

y = \frac{17 e ^{- 4 x^{3}}}{12} + \frac{7}{12}

y = \frac{17 e ^{- 4 x^{3}}}{12} + \frac{7}{12}

\frac{d y}{d x} = - y x

y^{^{'}} + 9 x y = 8 x, y (0) = 6

\frac{d y}{d x} = \frac{3 x ^{2} + 4 x + 2}{2 y + 1}

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

\frac{d y}{d t} = \frac{2}{100} - \frac{3 y}{100}

What is the solution for (dy)/(dx)+12x^2y=7x^2,y(0)=2 ?
The solution for (dy)/(dx)+12x^2y=7x^2,y(0)=2 is y=(17e^{-4x^3})/(12)+7/12