y^'=5sqrt(xy)

Lösung

y^{^{'}} = 5 x y

y = \frac{25 x ^{3}}{9} + \frac{5 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

y^{'} (x) = 5 x y

Solve separable ODE:

y = \frac{25 x ^{3}}{9} + \frac{5 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{25 x ^{3}}{9} + \frac{5 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

\frac{d y}{d t} = 2 y, y (9) = 4

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

\frac{d P}{d t} = 1.1 P (1 - \frac{P}{5000})

x^{^{'}} = x^{2} \cdot \frac{1}{2}

y^{^{'}} + 16 x y = x