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Beliebt Rechnen >

(dy)/(dx)=(x^2+2)y^{1/2}

Lösung

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

Lösung

y = c_{1} x + \frac{x ^{4}}{3} + x^{2} + \frac{c _{1} x ^{3}}{6} + \frac{x ^{6}}{36} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

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

Solve separable ODE:

y = c_{1} x + \frac{x ^{4}}{3} + x^{2} + \frac{c _{1} x ^{3}}{6} + \frac{x ^{6}}{36} + \frac{c _{1}^{2}}{4}

y = c_{1} x + \frac{x ^{4}}{3} + x^{2} + \frac{c _{1} x ^{3}}{6} + \frac{x ^{6}}{36} + \frac{c _{1}^{2}}{4}

Graph

Beliebte Beispiele

(dy)/(dx)=-(y(1-x))/(x(1-y))

\frac{d y}{d x} = - \frac{y ( 1 - x )}{x ( 1 - y )}

y(dy)/(dx)-x^2=x^2y

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

(dy)/(dx)= 2/(5sqrt(xy))x,y>0

\frac{d y}{d x} = \frac{2}{5 x y} x, y > 0

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

\frac{d y}{d t} = 2 c - y