What is the solution for (dy)/(dx)+x^3y=2x^3 ?

The solution for (dy)/(dx)+x^3y=2x^3 is y=e^{-(x^4)/4+c_{1}}+2

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(dy)/(dx)+x^3y=2x^3

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

y = e^{- \frac{x ^{4}}{4} + c_{1}} + 2

Solution steps

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

Solve separable ODE:

y = e^{- \frac{x ^{4}}{4} + c_{1}} + 2

y = e^{- \frac{x ^{4}}{4} + c_{1}} + 2

3 x y^{^{'}} - 5 y = 0

x ln (x) = y (1 + 3 + y^{2}) y^{^{'}} (x), y (1) = 1

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

2 y y^{^{'}} = 3 x^{2}

(1 + y + y^{2}) d x + x (x^{2} - 4) d y = 0

What is the solution for (dy)/(dx)+x^3y=2x^3 ?
The solution for (dy)/(dx)+x^3y=2x^3 is y=e^{-(x^4)/4+c_{1}}+2