神马作文网matlab解二阶微分方程
来源：学生作业帮 编辑：神马作文网作业帮 分类：综合作业 时间：2024/11/15 22:22:18
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。
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。
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)
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)