(dy)/(dx)=xe^{5y-3x},y(0)=1

Lösung

\frac{d y}{d x} = x e^{5 y - 3 x}, y (0) = 1

y = - \frac{ln ( \frac{5 e ^{- 3 x} x}{3} + \frac{5}{9} e ^{- 3 x} + \frac{1}{e ^{5}} - \frac{5}{9} )}{5}

Schritte zur Lösung

\frac{d y}{d x} = x e^{5 y - 3 x}

Solve separable ODE:

y = - \frac{ln ( \frac{5 e ^{- 3 x} x}{3} + \frac{5}{9} e ^{- 3 x} + \frac{1}{e ^{5}} - \frac{5}{9} )}{5}

y = - \frac{ln ( \frac{5 e ^{- 3 x} x}{3} + \frac{5}{9} e ^{- 3 x} + \frac{1}{e ^{5}} - \frac{5}{9} )}{5}

y^{^{'}} = x^{6} y^{- 7}

2 x sin (3 y) d x + 3 x^{2} cos (3 y) d y = 0

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

0.001 \cdot y^{^{'}} + 0.001 \cdot y = 0

y^{^{'}} = - a y x