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

Lösung

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

y = - \frac{ln ( 2 e ^{- x} + e ^{2} - 2 )}{2}

Schritte zur Lösung

y^{'} (x) = e^{2 y - x}

Solve separable ODE:

y = - \frac{ln ( 2 e ^{- x} + e ^{2} - 2 )}{2}

y = - \frac{ln ( 2 e ^{- x} + e ^{2} - 2 )}{2}

y^{^{'}} \cdot y \cdot e^{x^{2}} - 2 x = 0

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

\frac{d y}{d x} = \frac{x - 8}{y ^{3}}

y^{^{'}} = y^{2} (9 x + 5)

y^{^{'}} sec (x) = 5 y^{2}, y (\frac{π}{2}) = \frac{1}{2}