(dy)/(dx)=sqrt(9/2 y)

Lösung

\frac{d y}{d x} = \frac{9}{2} y

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

Schritte zur Lösung

\frac{d y}{d x} = \frac{9}{2} y

Solve separable ODE:

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

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

y y^{^{'}} = x e^{y^{2}}

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

\frac{d y}{d x} = \frac{2 y}{( x + 1 ) + ( x + 1 ) ^{\frac{5}{2}}}

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

- y = k \frac{d y}{d x}