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

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

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

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

y = \frac{x ^{3}}{2} + \frac{c _{1} x ^{3}}{e ^{\frac{- 1 + c _{1} x ^{2}}{x ^{2}}}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{2} + \frac{c _{1} x ^{3}}{e ^{\frac{- 1 + c _{1} x ^{2}}{x ^{2}}}}

y = \frac{x ^{3}}{2} + \frac{c _{1} x ^{3}}{e ^{\frac{- 1 + c _{1} x ^{2}}{x ^{2}}}}

x \to 1 lim (\frac{x ^{3}}{x - 1})

\frac{2}{s - 3}

f (x) = x^{2} + 2, (5, 27)

10 sin (x) cos (x)

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

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