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

Lösung

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

y = \frac{3 + 9 - 4 ( - c _{1} - x - x ^{3} )}{2}, y = \frac{3 - 9 - 4 ( - c _{1} - x - x ^{3} )}{2}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{3 + 9 - 4 ( - c _{1} - x - x ^{3} )}{2}, y = \frac{3 - 9 - 4 ( - c _{1} - x - x ^{3} )}{2}

y = \frac{3 + 9 - 4 ( - c _{1} - x - x ^{3} )}{2}, y = \frac{3 - 9 - 4 ( - c _{1} - x - x ^{3} )}{2}

x^{2} y^{^{'}} = \frac{1}{y} x^{5}

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

4 y d x + x d y = 0

2 x y^{^{'}} = 4 - y^{2}

t \frac{d y}{d t} = 16 y