(dy)/(dx)=8sqrt(xy)

Lösung

\frac{d y}{d x} = 8 x y

y = \frac{64 x ^{3}}{9} + \frac{8 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d x} = 8 x y

Solve separable ODE:

y = \frac{64 x ^{3}}{9} + \frac{8 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{64 x ^{3}}{9} + \frac{8 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y^{^{'}} = y^{(\frac{1}{2})}

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

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

y^{^{'}} + \frac{y}{3} = 4, y (- 1) = 0

y^{^{'}} = 1 - y, y (0) = \frac{1}{2}