d/(dθ)(r(θ))=(r(θ)^2)/θ ,r(1)=2

Lösung

\frac{d r}{d θ} = \frac{r ^{2}}{θ}, r (1) = 2

r = 2 e^{\frac{θ ^{2} - 1}{2}}

Schritte zur Lösung

\frac{d r}{d θ} = \frac{r θ ^{2}}{θ}

Solve separable ODE:

r = 2 e^{\frac{θ ^{2} - 1}{2}}

r = 2 e^{\frac{θ ^{2} - 1}{2}}

x f^{^{'}} (x) = (f (x))^{2}

\frac{d y}{d x} = 8 x y - 12 x^{2} y

x^{2} + 1 d x - 3 y d y = 0

x^{^{'}} = x^{2} t

y \cdot d x = (- 1 + x) d y