y^'y=(4x^3+5)(4x^7-7)

Lösung

y^{^{'}} y = (4 x^{3} + 5) (4 x^{7} - 7)

y = \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}, y = - \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}

Schritte zur Lösung

y^{'} (x) y = (4 x^{3} + 5) (4 x^{7} - 7)

Solve separable ODE:

y = \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}, y = - \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}

y = \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}, y = - \frac{32 x ^{11}}{11} - 14 x^{4} + 5 x^{8} - 70 x + c_{1}

4 (5 x - 3)^{2} \frac{d y}{d x} = 2 y - 4

\frac{d y}{d x} = \frac{2 ( 5 - y )}{x}

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

(1 + x^{2}) y^{^{'}} = - 4 x y

1 = \frac{cos ( y )}{x ^{2} sin ( y )} \frac{d y}{d x}, sin (y) > 0