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Beliebt Rechnen >

(sqrt(x)+x)*(dy)/(dx)=sqrt(y)+y

Lösung

(x + x) \cdot \frac{d y}{d x} = y + y

Lösung

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

Schritte zur Lösung

(x + x) \cdot \frac{d y}{d x} = y + y

Solve separable ODE:

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

Graph

Beliebte Beispiele

y^{^{'}} = y (3 t - 30)

(dx)/(dt)=10-(70x)/(100)

\frac{d x}{d t} = 10 - \frac{70 x}{100}

y^{^{'}} = 12 x^{3} e^{y}

(dy)/(dx)=-(9/6)^2y^6

\frac{d y}{d x} = - (\frac{9}{6})^{2} y^{6}

(dy)/(dx)-(xy)/(1-x^2)=(xy^2)/(1-x^2)

\frac{d y}{d x} - \frac{x y}{1 - x ^{2}} = \frac{x y ^{2}}{1 - x ^{2}}