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Beliebt Rechnen >

e^ty^'=(1+y^2)t

Lösung

e^{t} y^{^{'}} = (1 + y^{2}) t

Lösung

y = tan (\frac{- t - 1}{e ^{t}} + c_{1})

Schritte zur Lösung

e^{t} y^{'} (t) = (1 + y^{2}) t

Solve separable ODE:

y = tan (\frac{- t - 1}{e ^{t}} + c_{1})

y = tan (\frac{- t - 1}{e ^{t}} + c_{1})

Graph

Beliebte Beispiele

x^2y^'=y^2,y(1)=-1

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

y^'= x/y ,y(0)=-3

y^{^{'}} = \frac{x}{y}, y (0) = - 3

d/(dt)(\H(t))=4-0.5\H(t),\H(0)=0

\frac{d}{d t} (H (t)) = 4 - 0.5 H (t), H (0) = 0

(dy)/(dx)=(10+16x)/(xy^2),y=4,x=1

\frac{d y}{d x} = \frac{10 + 16 x}{x y ^{2}}, y = 4, x = 1

y^2+y-x(dy)/(dx)=0

y^{2} + y - x \frac{d y}{d x} = 0