y^'=2x*cosh^2(y)

Lösung

y^{^{'}} = 2 x \cdot cosh^{2} (y)

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

Schritte zur Lösung

y^{'} (x) = 2 x \cdot cosh^{2} (y)

Solve separable ODE:

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

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

\frac{d y}{d x} = 2 x y^{2}, y = - 1, x = 1

y^{^{'}} = 5 e^{x - y}

\frac{d y}{d t} = - \frac{t}{2 y}

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

y^{^{'}} = \frac{x ^{3}}{y}