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Beliebt Rechnen >

(1+t^2)*(dy)/(dt)=1+y^2

Lösung

(1 + t^{2}) \cdot \frac{d y}{d t} = 1 + y^{2}

Lösung

y = tan (arctan (t) + c_{1})

Schritte zur Lösung

(1 + t^{2}) \cdot \frac{d y}{d t} = 1 + y^{2}

Solve separable ODE:

y = tan (arctan (t) + c_{1})

y = tan (arctan (t) + c_{1})

Graph

Beliebte Beispiele

(dy)/(dx)=(4y+1)/(3x-2)

\frac{d y}{d x} = \frac{4 y + 1}{3 x - 2}

ln(x)(dx)/(dy)= x/y

ln (x) \frac{d x}{d y} = \frac{x}{y}

y^'+tan(3*x)y=0

y^{^{'}} + tan (3 \cdot x) y = 0

y^{^{'}} = 3 y - 4

(1+y^2)cos(x)dx-1xdy=0,y(0)= pi/4

(1 + y^{2}) cos (x) d x - 1 x d y = 0, y (0) = \frac{π}{4}