What is the solution for (dy)/(dx)=(x^2+7x+3)/(y^2) ?

The solution for (dy)/(dx)=(x^2+7x+3)/(y^2) is y=\sqrt[3]{x^3+(21x^2)/2+9x+c_{1}}

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(dy)/(dx)=(x^2+7x+3)/(y^2)

\frac{d y}{d x} = \frac{x ^{2} + 7 x + 3}{y ^{2}}

y = 3 x^{3} + \frac{21 x ^{2}}{2} + 9 x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x ^{2} + 7 x + 3}{y ^{2}}

Solve separable ODE:

y = 3 x^{3} + \frac{21 x ^{2}}{2} + 9 x + c_{1}

y = 3 x^{3} + \frac{21 x ^{2}}{2} + 9 x + c_{1}

(x y^{2} - x) d x + (2 x^{2} + 4) d y = 0

\frac{d y}{d x} = \frac{3 x ^{2} - e ^{x}}{2 y - 5}

(x^{2} y + 2 y) y^{^{'}} = 2 x y^{2} + 2 x

y = x \cdot y^{^{'}}

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

What is the solution for (dy)/(dx)=(x^2+7x+3)/(y^2) ?
The solution for (dy)/(dx)=(x^2+7x+3)/(y^2) is y=\sqrt[3]{x^3+(21x^2)/2+9x+c_{1}}