((dy))/((dx))=(2x+10)*e^{-y},y(0)=0

Lösung

\frac{( d y )}{( d x )} = (2 x + 10) \cdot e^{- y}, y (0) = 0

y = ln (x^{2} + 10 x + c_{1})

Schritte zur Lösung

\frac{( d y )}{( d x )} = (2 x + 10) \cdot e^{- y}

Solve separable ODE:

y = ln (x^{2} + 10 x + c_{1})

y = ln (x^{2} + 10 x + c_{1})

y^{^{'}} - 2 y = 2 y^{\frac{1}{2}}

y^{2} y^{^{'}} = 2 (t + t y^{3}) e^{t^{2}}

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

3 \frac{d x}{d t} + 2 x = 4, x = 0

u^{^{'}} = 2 e^{3 x - H (x)}