y^'=(x^2-3)/(y^2),y(0)=6

Lösung

y^{^{'}} = \frac{x ^{2} - 3}{y ^{2}}, y (0) = 6

y = 3 x^{3} - 9 x + 216

Schritte zur Lösung

y^{'} (x) = \frac{x ^{2} - 3}{y ^{2}}

Solve separable ODE:

y = 3 x^{3} - 9 x + 216

y = 3 x^{3} - 9 x + 216

y^{^{'}} = 3 \cdot y

y^{^{'}} = \frac{y ^{4} 2 x}{4 y ^{3} x ^{2}}

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

\frac{d y}{y} = d x (x - 1)

\frac{d y}{d x} y = ln (7) x^{2}