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

The solution for (dy)/(dx)=(x^2+3x-1)/(y^2) is y=\sqrt[3]{x^3+(9x^2)/2-3x+c_{1}}

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(dy)/(dx)=(x^2+3x-1)/(y^2)

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

y = 3 x^{3} + \frac{9 x ^{2}}{2} - 3 x + c_{1}

Solution steps

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

Solve separable ODE:

y = 3 x^{3} + \frac{9 x ^{2}}{2} - 3 x + c_{1}

y = 3 x^{3} + \frac{9 x ^{2}}{2} - 3 x + c_{1}

y^{^{'}} - x \cdot e^{y} = 0, y (0) = 2

\frac{d p}{d t} = 4 pt, p (1) = 7

y^{^{'}} = (sin (x)) (cos^{2} (x)) (tan (y))

\frac{d y}{d x} = y (- 8 - y)

(y^{2} + 2) d x + 3 \cdot x \cdot y d y = 0

What is the solution for (dy)/(dx)=(x^2+3x-1)/(y^2) ?
The solution for (dy)/(dx)=(x^2+3x-1)/(y^2) is y=\sqrt[3]{x^3+(9x^2)/2-3x+c_{1}}