x^2dx-(y+x^3y)dy=0

Lösung

x^{2} d x - (y + x^{3} y) d y = 0

y = \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}, y = - \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}

Schritte zur Lösung

x^{2} d x - (y + x^{3} y) d y = 0

Solve separable ODE:

y = \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}, y = - \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}

y = \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}, y = - \frac{2 ln ( ( x + 1 ) ( x ^{2} - x + 1 ) ) + c _{1}}{3}

\frac{d x}{d t} = (1 + t) (1 + x)

y^{^{'}} = 3 y, y (0) = 5

y^{^{'}} = 3 y, y (0) = 3

y^{^{'}} = \frac{y ^{2} - 3}{( 2 x y )}

y^{^{'}} + y \frac{1 + 6 t ^{2}}{2 t + 3 t ^{3}} = 0