y^'=e^{-y}sin(x),y(pi/2)= 1/2

Lösung

y^{^{'}} = e^{- y} sin (x), y (\frac{π}{2}) = \frac{1}{2}

y = ln (- cos (x) + e^{\frac{1}{2}})

Schritte zur Lösung

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

Solve separable ODE:

y = ln (- cos (x) + e^{\frac{1}{2}})

y = ln (- cos (x) + e^{\frac{1}{2}})

y^{^{'}} + 2 y = 0, y (0) = 1.5

\frac{d y}{d x} + x^{2} y = 0

3 (x^{2} + 1) \frac{d y}{d x} = 2 x y (y^{3} - 1)

\frac{d y}{d x} x y + x = 2

x^{^{'}} = x