What is the solution for x((dy)/(dx))-3y=x^3,y(1)=1 ?

The solution for x((dy)/(dx))-3y=x^3,y(1)=1 is y=x^3ln(x)+x^3

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x((dy)/(dx))-3y=x^3,y(1)=1

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

y = x^{3} ln (x) + x^{3}

Solution steps

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

Solve linear ODE:

y = x^{3} ln (x) + x^{3}

y = x^{3} ln (x) + x^{3}

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

x \to 0 + lim (\frac{ln ( x )}{x ^{2}})

\frac{d y}{d t} = 5 y + y^{5}

x - \frac{1}{3 x ^{3}}

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

What is the solution for x((dy)/(dx))-3y=x^3,y(1)=1 ?
The solution for x((dy)/(dx))-3y=x^3,y(1)=1 is y=x^3ln(x)+x^3