(dy)/(dx)= x/(y+x^2y),y(0)=2

Lösung

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

y = ln (1 + x^{2}) + 4

Schritte zur Lösung

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

Solve separable ODE:

y = ln (1 + x^{2}) + 4

y = ln (1 + x^{2}) + 4

y^{^{'}} + y = y (t e^{t^{2}} + 1)

\frac{d v}{d t} + 2 v = 0

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

y^{^{'}} = 8 y - 10

x y^{2} - 7 y^{2} - x^{2} \frac{d y}{d x} = 0