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Beliebt Rechnen >

(ydy)/(xdx)=(sqrt(y^2+1))/(sqrt(x^2+1))

Lösung

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

Lösung

y = x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}, y = - x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}

Schritte zur Lösung

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

Solve separable ODE:

y = x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}, y = - x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}

y = x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}, y = - x^{2} + 2 c_{1} x^{2} + 1 + c_{1}^{2}

Graph

Beliebte Beispiele

[k*f(x)]=k*f^'(x)

[k \cdot f (x)] = k \cdot f^{^{'}} (x)

y^{^{'}} = \frac{1}{4} y^{2}

(t^2-22t+96)y^'=y

(t^{2} - 22 t + 96) y^{^{'}} = y

5dx-e^{y-x}dy=0

5 d x - e^{y - x} d y = 0

(dy)/(dx)=3x^2y,y=9,x=0

\frac{d y}{d x} = 3 x^{2} y, y = 9, x = 0