What is the solution for (dy)/(dx)+x^2y=1 ?

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

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(dy)/(dx)+x^2y=1

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

y = \frac{\int e ^{\frac{x ^{3}}{3}} d x}{e ^{\frac{x ^{3}}{3}}}

Solution steps

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

Solve linear ODE:

y = \frac{\int e ^{\frac{x ^{3}}{3}} d x}{e ^{\frac{x ^{3}}{3}}}

y = \frac{\int e ^{\frac{x ^{3}}{3}} d x}{e ^{\frac{x ^{3}}{3}}}

x \to 0 lim (8^{- x})

3 ln (x) - \frac{x ^{2}}{24}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x} + e^{2 x} + e^{- x}

\frac{x ^{2}}{1 + 2 x}

(6 y + 2 x - 7) d x + (8 y + 6 x - 1) d y = 0

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