[試題] 97上 李克強 工程數學 期中考
課程名稱︰工程數學
課程性質︰系定必修
課程教師︰李克強
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2008/10/31
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(一) Find the solution of the following differential equations:
(1) dy 2x
── = ──── (5%)
dx y+x^(2)y
(2) dy
(9x^(2)+y-1)-(4y-x)── = 0 (5%)
dx
(3) dy ┌ 4x+3y ┐
── = -│ ───── │ (5%)
dx └ 2x+y ┘
(4) dy y
── - ── +y^(2) = 0 (5%)
dx x
(5) dy
── + y = x^(2)+x+1 (5%)
dx
(二) Find the second solution of the following differential equation by the
method of reduction of order:(10%)
x^(2)y"-x(x+2)y'+(x+2)y=0 , x>0
with y1(x)=x as the given first solution.
(三) Find the general solutions of the following differential equations:
(A) 2y"+3y'+y=x^(2) + 3sinx (10%)
(B) y"-2y'+y = xe^(x)+ 4 (10%)
(C) (x-1)^(2)y"+8(x-1)y'+12y=0 , x≠0 (10%)
(D) x^(2)y"-3xy'+ 4y = ㏑x ,x>0 (10%)
(E) x^(3)y'" + x^(2)y"+xy'-y=1 , x>1 (10%)
(F) x^(3)y'"-3x^(2)y"+6xy'-6y=e^(x)（x^(5)+x^(4)）, x>0 (15%)
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