Question

matlab解二阶微分方程

怎么用matlab来解呢？
x的定义域是（0，l），i是道路横坡坡度，w是降雨强度，k是路面横向渗透系数。

Answer 1

你的方程即为：
y'*y' + y''*y' +w/k =0

s = dsolve('Dy*D2y + Dy^2 + w/k ', 'y(l) = a', 'Dy(0) = i1','x'); % i1即i

用2011b可得如下结果：

a + (exp(log(k*i1^2 + w) - 2*l) - w)^(1/2)/k^(1/2) - (exp(log(k*i1^2 + w) - 2*x) - w)^(1/2)/k^(1/2) - (w^(1/2)*atan(((k*i1^2 + w)/exp(2*l) - w)^(1/2)/w^(1/2)))/k^(1/2) + (w^(1/2)*atan(((k*i1^2 + w)/exp(2*x) - w)^(1/2)/w^(1/2)))/k^(1/2)
a - (exp(log(k*i1^2 + w) - 2*l) - w)^(1/2)/k^(1/2) + (exp(log(k*i1^2 + w) - 2*x) - w)^(1/2)/k^(1/2) + (w^(1/2)*atan(((k*i1^2 + w)/exp(2*l) - w)^(1/2)/w^(1/2)))/k^(1/2) - (w^(1/2)*atan(((k*i1^2 + w)/exp(2*x) - w)^(1/2)/w^(1/2)))/k^(1/2)

Answer 2

desolve(y*Dy-i)