Re: [工數]ODE
※ 引述《miniye ()》之銘言:
: http://www.lib.nthu.edu.tw/library/department/ref/exam/ns/ns/98/2303_2502.pdf
: 第六題後面一直解不出來
: 拜託各位
: 我只解到積分因子是X^2
: 但後面就解不出來了
integrator factor I(x) = x^2
M'(x,y) = M(x,y)*I(x) = 2xe^xy + (x^2)ye^xy + 3x^2(siny) + x
N'(x,y) = N(x,y)*I(x) = (x^3)e^xy + (x^3)cosy
M'y = N'x → exact
↑
M'(x,y)對y偏微
fy = N'(x,y)
↑原ode f(x,y)對y偏微
df = [(x^3)e^xy + (x^3)cosy]dy
f(x,y) = (x^2)e^xy + (x^3)siny + g(x)
fx = M'(x,y)
↑f(x,y)對x偏微
可以得到 g'(x) = x
所以 g(x) = 0.5x^2 + constanst
所以 f(x,y) = (x^2)e^xy + (x^3)siny + 0.5x^2 = c #
有錯還煩請高手不吝於指正 <(_ _)>
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01/22 23:17, , 1F
01/22 23:17, 1F
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