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Beliebt Rechnen >

(1-t^2)y^'-t^2y=(1+t)*(sqrt(1-t^2))

Lösung

(1 - t^{2}) y^{^{'}} - t^{2} y = (1 + t) \cdot (1 - t^{2})

Lösung

y = \frac{t + 1 \cdot \int \frac{e ^{t + c_{1}} t - 1 1 + t}{1 - t ^{2}} d t}{e ^{t + c_{1}} t - 1}

Schritte zur Lösung

(1 - t^{2}) y^{'} (t) - t^{2} y = (1 + t) \cdot (1 - t^{2})

Solve linear ODE:

y = \frac{t + 1 \cdot \int \frac{e ^{t + c_{1}} t - 1 1 + t}{1 - t ^{2}} d t}{e ^{t + c_{1}} t - 1}

y = \frac{t + 1 \cdot \int \frac{e ^{t + c_{1}} t - 1 1 + t}{1 - t ^{2}} d t}{e ^{t + c_{1}} t - 1}

Beliebte Beispiele

tangent 3x^2+y^2=1,(1/2 ,(-1)/2)

t an g e n t 3 x^{2} + y^{2} = 1, (\frac{1}{2}, \frac{- 1}{2})

y^{''}-y^'+12y=0

y^{^{''}} - y^{^{'}} + 12 y = 0

derivative of ((e^x)/(1-e^{-x)})

\frac{d}{d x} (\frac{( e ^{x} )}{1 - e ^{- x}})

integral of-x/(x^2+y^2)

\int - \frac{x}{x ^{2} + y ^{2}} d x

y^{^{'}} + \frac{y}{t} = 2 e^{t}