Question

常微分方程？

如图，求解 谢谢

Answer 1

Answer 2

化简一下：
dv * 2v/(-2v²+3v+2) = dt/t
-dv * 2v/[(2v+1)(v-2)] = dt/t
-dv * [0.4/(2v+1) + 0.8/(v-2)] = dt/t
-0.4dv/(2v+1) - 0.8dv/(v-2) = dt/t
-0.2 *d(2v+1)/(2v+1) - 0.8 * d(v-2)/(v-2) = dt/t
这个方程两边同时积分，可以得到：
-0.2*∫d(2v+1)/(2v+1) - 0.8 *∫d(v-2)/(v-2) = ∫dt/t
-0.2 * ln(2v+1) - 0.8 * ln(v-2) = ln(t) + c
-0.2 * [ln(2v+1) + 4*ln(v-2)] = ln(t) + c
ln[(2v+1) * (v-2)^4] = -5 * ln(t) - 5c
(2v+1) * (v-2)^4 = 1/t^5 * e^(-5c) = C/t^5