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Matlab题:求解初值问题{y'=(y-3x/y)3/2(0
题目详情
Matlab题:求解初值问题{y'=(y-3x/y)3/2 (0
▼优质解答
答案和解析
y/x=t
dy/dx=t+xdt/dx
2/3t+2/3xdt/dx=xt-3/t
2/3xdt/dx=t(x-1)
2/3dt/t=(x-1)/xdx
2t/3=x-lnx+lnc
t=3/2(x-ln(x/c))
y/x=3/2(x-ln(x/c))
y=3/2x(x-ln(x/c))
dy/dx=t+xdt/dx
2/3t+2/3xdt/dx=xt-3/t
2/3xdt/dx=t(x-1)
2/3dt/t=(x-1)/xdx
2t/3=x-lnx+lnc
t=3/2(x-ln(x/c))
y/x=3/2(x-ln(x/c))
y=3/2x(x-ln(x/c))
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