y^'=((2y+3)/(4x+5))^2

Lösung

y^{^{'}} = (\frac{2 y + 3}{4 x + 5})^{2}

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

Schritte zur Lösung

y^{'} (x) = (\frac{2 y + 3}{4 x + 5})^{2}

Solve separable ODE:

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

y = - \frac{4 x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{24 c _{1} x}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{30 c _{1}}{- 1 + 16 c _{1} x + 20 c _{1}} - \frac{7}{2 ( - 1 + 16 c _{1} x + 20 c _{1} )}

\int \frac{1}{( 25 x ^{2} + 4 ) ^{2}} d x

d er i v a t i v e f (x) = (3 x^{3} + 9 x + 7) (x^{2} + 8)

so l v e f or x, f = f e^{\frac{1}{f}}

x \to - 2 - lim ([x])

d er i v a t i v e 2 + \frac{2}{x} + \frac{6}{x ^{2}}