(dy)/((6+y)^2)=(dx)/((10+9x)^4)

解答

\frac{d y}{( 6 + y ) ^{2}} = \frac{d x}{( 10 + 9 x ) ^{4}}

y = - \frac{19683 x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{118098 c _{1} x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{65610 x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{393660 c _{1} x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{72900 x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{437400 c _{1} x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{162000 c _{1}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{26994}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}}

求解步骤

\frac{d y}{( 6 + y ) ^{2}} = \frac{d x}{( 10 + 9 x ) ^{4}}

求解可分离方程:

y = - \frac{19683 x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{118098 c _{1} x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{65610 x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{393660 c _{1} x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{72900 x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{437400 c _{1} x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{162000 c _{1}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{26994}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}}

y = - \frac{19683 x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{118098 c _{1} x ^{3}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{65610 x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{393660 c _{1} x ^{2}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{72900 x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{437400 c _{1} x}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{162000 c _{1}}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}} - \frac{26994}{- 1 + 19683 c _{1} x ^{3} + 65610 c _{1} x ^{2} + 72900 c _{1} x + 27000 c _{1}}

\frac{df}{d θ} = sin (θ) + csc (θ)

\int (2 x^{3} - 5 x + 7) d x

\frac{d}{d v} (u \cdot v)

d er i v a t i v e f (θ) = 4 sin (θ) - θ

y + (x + 1) \frac{d y}{d x} = 2 x + 2, y (0) = 2