(yx^2-y)dy=arctan(x)dx

Lösung

(y x^{2} - y) d y = arctan (x) d x

y = 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x, y = - 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x

Schritte zur Lösung

(y x^{2} - y) d y = arctan (x) d x

Solve separable ODE:

y = 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x, y = - 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x

y = 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x, y = - 2 \cdot \int \frac{arctan ( x )}{( x + 1 ) ( x - 1 )} d x

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

y^{^{'}} = - y \cdot cos (x)

y^{2} sec (5 x) \frac{d y}{d x} = 1, y (0) = 0

\frac{d y}{d x} = \frac{- e ^{x} ( y - 1 )}{2 ( e ^{x} + 4 )}

y^{^{'}} cos (y) + 2 x sin (y) = - 2 x