y^'=xy^{1/2}

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x y d y + y d x + 4 y d y + 3 d x = 8 d y + 3 x d x + 2 x d y + x y d x

f (x) = \frac{df}{d x}

x y^{^{'}} = (x + 1) y

\frac{d y}{d x} + y = 1, y (0) = 0

y^{^{'}} = 15 y - y^{2} - 50