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

Lösung

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

\frac{\partial}{\partial y} ((x + 2 y)^{2})

\frac{d}{d x} (\frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}})

\int \frac{( 5 x ^{2} )}{1 - 5 x ^{3}} d x

x \to 0 + lim (sin (\frac{π}{x}))

\frac{\partial}{\partial x} (y - x^{2})