(dy)/(dx)=((2y+5)^2)/((8x+9)^2)

Lösung

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}

Schritte zur Lösung

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

Solve separable ODE:

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}

y = - \frac{16 x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{160 c _{1} x}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{180 c _{1}}{- 1 + 64 c _{1} x + 72 c _{1}} - \frac{31}{2 ( - 1 + 64 c _{1} x + 72 c _{1} )}

t an g e n t y = x^{2}, (2, 4)

x \to 3 lim (\frac{x ^{2} - 3 x}{x - 3})

x \to 0 lim ((e^{x} + x)^{\frac{5}{x}})

\int sin^{2} (2 π x) d x

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})