y^5(dy)/(dx)=4x^2y^6-12x^2

Lösung

y^{5} \frac{d y}{d x} = 4 x^{2} y^{6} - 12 x^{2}

y = 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}

Schritte zur Lösung

y^{5} \frac{d y}{d x} = 4 x^{2} y^{6} - 12 x^{2}

Solve separable ODE:

y = 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}

y = 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{8 x^{3} + c_{1}} + 33 \cdot 3^{\frac{2}{3}}

y^{^{'}} - 3 x y^{2} = 2 x

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

\frac{d y}{d x} + 6 x^{2} y = 9 x^{2}

\frac{d P}{d t} = 8 Pt, P (1) = 3

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