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

Lösung

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

y = \frac{3 c _{1} x}{- 5 + c _{1} x - 3 c _{1}} - \frac{x}{- 5 + c _{1} x - 3 c _{1}} - \frac{9 c _{1}}{- 5 + c _{1} x - 3 c _{1}} - \frac{12}{- 5 + c _{1} x - 3 c _{1}}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{3 c _{1} x}{- 5 + c _{1} x - 3 c _{1}} - \frac{x}{- 5 + c _{1} x - 3 c _{1}} - \frac{9 c _{1}}{- 5 + c _{1} x - 3 c _{1}} - \frac{12}{- 5 + c _{1} x - 3 c _{1}}

y = \frac{3 c _{1} x}{- 5 + c _{1} x - 3 c _{1}} - \frac{x}{- 5 + c _{1} x - 3 c _{1}} - \frac{9 c _{1}}{- 5 + c _{1} x - 3 c _{1}} - \frac{12}{- 5 + c _{1} x - 3 c _{1}}

\frac{d}{d x} (\frac{7}{10} x^{2} + 4^{3})

\frac{d y}{d x} = \frac{18 ( 2 + y ) ^{2}}{( 1 - 3 x ) ^{2}}

\int (x^{2} - 2 x + 3) ln (x) d x

x \to 0 lim (3 (x^{\frac{x}{2}}))

t an g e n t f (x) = \frac{6}{5 x + 3}, at x = - 1