(dy)/(dx)=(e^{5x})/(cos(2y))

Lösung

\frac{d y}{d x} = \frac{e ^{5 x}}{cos ( 2 y )}

y = \frac{arcsin ( \frac{2}{5} e ^{5 x} + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - \frac{2}{5} e ^{5 x} - c _{1} )}{2} + πn

Schritte zur Lösung

\frac{d y}{d x} = \frac{e ^{5 x}}{cos ( 2 y )}

Solve separable ODE:

y = \frac{arcsin ( \frac{2}{5} e ^{5 x} + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - \frac{2}{5} e ^{5 x} - c _{1} )}{2} + πn

y = \frac{arcsin ( \frac{2}{5} e ^{5 x} + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - \frac{2}{5} e ^{5 x} - c _{1} )}{2} + πn

y^{^{'}} - 2 x^{2} y - y = 0

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

y y^{^{'}} = [sin (x) - cos (x)] 1 - y^{2}

\frac{d y}{d x} = 13 x sec (y)

3 y^{^{'}} = e^{x - 3 y}