x^2(dy)/(dx)+3xy=x

Lösung

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

y = - \frac{c _{1}}{3 x ^{3}} + \frac{1}{3}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{c _{1}}{3 x ^{3}} + \frac{1}{3}

y = - \frac{c _{1}}{3 x ^{3}} + \frac{1}{3}

\frac{d y}{d x} = 12 x^{3} y, y (0) = 2

y^{^{'}} - 3 x y = 0

(x + 1) \frac{d y}{d x} + 1 = 2 e^{- y}

y^{^{'}} = 3 x^{2} (y^{2} + 1)

x y^{2} d x + (x^{2} y + 3 y) d y = 0, y (1) = 1