What is the solution for (dy)/(dx)-1/x*y-3*x^2=0 ?

The solution for (dy)/(dx)-1/x*y-3*x^2=0 is y=(3x^3)/2+c_{1}x

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(dy)/(dx)-1/xy-3x^2=0

\frac{d y}{d x} - \frac{1}{x} \cdot y - 3 \cdot x^{2} = 0

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

Solution steps

\frac{d y}{d x} - \frac{1}{x} \cdot y - 3 \cdot x^{2} = 0

Solve linear ODE:

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

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

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

f (x) = \frac{7 x}{x + 4}, at x = 3

\int sin^{3} (3 x) cos^{2} (3 x) d x

f (x) = \frac{6 x}{x + 3}, (- 1, - 3)

\int e^{x} sin (3 x) d x

What is the solution for (dy)/(dx)-1/x*y-3*x^2=0 ?
The solution for (dy)/(dx)-1/x*y-3*x^2=0 is y=(3x^3)/2+c_{1}x