9t^2(dx)/(dt)+8x+8=0

Lösung

9 t^{2} \frac{d x}{d t} + 8 x + 8 = 0

x = e^{\frac{8}{9 t} + c_{1}} - 1

Schritte zur Lösung

9 t^{2} \frac{d x}{d t} + 8 x + 8 = 0

Solve separable ODE:

x = e^{\frac{8}{9 t} + c_{1}} - 1

x = e^{\frac{8}{9 t} + c_{1}} - 1

x^{^{'}} - c x = 0

y^{^{'}} + sin (t) y = - sin (t), y (0) = 9

x (x - 1) y + x y^{^{'}} + 2 y = 0

\frac{d y}{d t} = \frac{t}{t ^{2} y - y}

3 y y^{^{'}} = 4, x^{3} + 7 x y = 1