(x^2+4)dy+(8xy-2x)dx=0

Lösung

(x^{2} + 4) d y + (8 x y - 2 x) d x = 0

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

Schritte zur Lösung

(x^{2} + 4) d y + (8 x y - 2 x) d x = 0

Solve separable ODE:

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

y^{^{'}} + 2 y - 5 = 0

\frac{d y}{d x} y = \frac{6 x ^{2} + 4 x ^{2}}{3 y ^{6}}

y^{2} y^{^{'}} = x^{2} + 6 e^{x}

y^{^{'}} + y = 0, y (1) = 1

x (3 y^{2} - 2) y^{^{'}} (x) - y^{3} = 0, y (1) = 2