(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}

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

1 + y^{2} + x y y^{^{'}} = 0

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

3 (1 + t^{2}) d y = 2 t y (y^{3} - 1) d t

y^{^{'}} = y^{2} - 9