(dy)/(dx)=((1+2x)sqrt(y))

Lösung

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

y = \frac{c _{1} x ^{2}}{2} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + \frac{c _{1} x}{2} + \frac{x ^{2}}{4} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{c _{1} x ^{2}}{2} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + \frac{c _{1} x}{2} + \frac{x ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{c _{1} x ^{2}}{2} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + \frac{c _{1} x}{2} + \frac{x ^{2}}{4} + \frac{c _{1}^{2}}{4}

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

y^{^{'}} = y ln (y) cot (x)

\frac{d y}{d t} = - \frac{y}{( \frac{4320}{7} )}

2 x^{4} y \frac{d y}{d x} + 4 x^{3} y^{2} = 0

y^{^{'}} + \frac{y}{3} = 5, y (- 1) = 0