(dx)/(dy)xy-y^7=8y

Lösung

\frac{d x}{d y} x y - y^{7} = 8 y

x = 16 y + \frac{2 y ^{7}}{7} + c_{1}, x = - 16 y + \frac{2 y ^{7}}{7} + c_{1}

Schritte zur Lösung

\frac{d x}{d y} x y - y^{7} = 8 y

Solve separable ODE:

x = 16 y + \frac{2 y ^{7}}{7} + c_{1}, x = - 16 y + \frac{2 y ^{7}}{7} + c_{1}

x = 16 y + \frac{2 y ^{7}}{7} + c_{1}, x = - 16 y + \frac{2 y ^{7}}{7} + c_{1}

x y^{^{'}} + y = 4

y^{^{'}} = 15 4 x y

(y^{4} + 1) d x + x y^{3} d y = 0

y^{^{'}} + 6 y tan (2 x) = 0

y^{^{'}} = y ln (x) + y