(dy)/(dx)=(-4y+9)/(5x+4)

Lösung

\frac{d y}{d x} = \frac{- 4 y + 9}{5 x + 4}

y = \frac{c _{1}}{4 ( 5 x + 4 ) ^{\frac{4}{5}}} + \frac{9}{4}

Schritte zur Lösung

\frac{d y}{d x} = \frac{- 4 y + 9}{5 x + 4}

Solve separable ODE:

y = \frac{c _{1}}{4 ( 5 x + 4 ) ^{\frac{4}{5}}} + \frac{9}{4}

y = \frac{c _{1}}{4 ( 5 x + 4 ) ^{\frac{4}{5}}} + \frac{9}{4}

2 y + 3 + (2 x - 5) \frac{d y}{d x} = 0

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

y^{^{'}} = \frac{6 x - 3}{y}

y^{^{'}} = \frac{x}{y e ^{y + x^{2}}}

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