What is the solution for (dy)/(dx)=(x^2-7)/(y^2),y(0)=5 ?

The solution for (dy)/(dx)=(x^2-7)/(y^2),y(0)=5 is y=\sqrt[3]{x^3-21x+125}

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(dy)/(dx)=(x^2-7)/(y^2),y(0)=5

\frac{d y}{d x} = \frac{x ^{2} - 7}{y ^{2}}, y (0) = 5

y = 3 x^{3} - 21 x + 125

Solution steps

\frac{d y}{d x} = \frac{x ^{2} - 7}{y ^{2}}

Solve separable ODE:

y = 3 x^{3} - 21 x + 125

y = 3 x^{3} - 21 x + 125

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

sin (x) cos (x) y^{^{'}} - sin (y) cos (x) = 0

y^{^{'}} = \frac{1}{2} (k - y)

\frac{d y}{d x} = 6 e^{2 x - y}, y (0) = 0

5 x y d x - ln^{8} (y) d y = 0

What is the solution for (dy)/(dx)=(x^2-7)/(y^2),y(0)=5 ?
The solution for (dy)/(dx)=(x^2-7)/(y^2),y(0)=5 is y=\sqrt[3]{x^3-21x+125}