(dy)/(dx)=2e^{x-y},y(0)=ln(8)

Lösung

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (8)

y = ln (2 e^{x} + 6)

Schritte zur Lösung

\frac{d y}{d x} = 2 e^{x - y}

Solve separable ODE:

y = ln (2 e^{x} + 6)

y = ln (2 e^{x} + 6)

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

2 y^{^{'}} = y + 1

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

(1 + x) y + (1 - y) x y^{^{'}} = 0

y^{^{'}} = \frac{2 y ^{2} - 9}{( 3 x y )}