(dy)/(dx)=16sqrt(xy)

Lösung

\frac{d y}{d x} = 16 x y

y = \frac{256 x ^{3}}{9} + \frac{16 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d x} = 16 x y

Solve separable ODE:

y = \frac{256 x ^{3}}{9} + \frac{16 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{256 x ^{3}}{9} + \frac{16 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

x y^{^{'}} - y^{^{'}} \cdot ln (x) + y = 0

y = 1 - y^{^{'}} x

\frac{d p}{d t} = (1 - p)

\frac{d y}{y} = sin (x) d x

y^{^{'}} = - sin (y)