(dy)/(dx)=(((y+3))/((2x+5)))^2

Lösung

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

y = - \frac{4 x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{12 c _{1} x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{30 c _{1}}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{7}{- 1 + 4 c _{1} x + 10 c _{1}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{4 x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{12 c _{1} x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{30 c _{1}}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{7}{- 1 + 4 c _{1} x + 10 c _{1}}

y = - \frac{4 x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{12 c _{1} x}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{30 c _{1}}{- 1 + 4 c _{1} x + 10 c _{1}} - \frac{7}{- 1 + 4 c _{1} x + 10 c _{1}}

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

\frac{d}{d x} (4 x + 10)

\int_{2}^{6} (\frac{x}{2} + 1) d x

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

y^{^{''}} + 6 y^{^{'}} + 90 y = 0