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Beliebt Rechnen >

xy^'=y^2-1

Lösung

x y^{^{'}} = y^{2} - 1

Lösung

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

Schritte zur Lösung

x y^{'} (x) = y^{2} - 1

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(x^3+1)/(x^2)(dy)/(dx)= 1/y

\frac{x ^{3} + 1}{x ^{2}} \frac{d y}{d x} = \frac{1}{y}

y y^{^{'}} = - 5 x

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

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

(y^2+3)dx=ysec^2(x)dy

(y^{2} + 3) d x = y sec^{2} (x) d y

(x^3+x^3)dx=xy^2dy

(x^{3} + x^{3}) d x = x y^{2} d y