[试题] 108-1 颜炳郎 工程数学 第一次小考

楼主: unmolk (UJ)   2020-01-17 01:19:12
课程名称︰工程数学
课程性质︰生机系必修
课程教师︰颜炳郎
开课学院:生农学院
开课系所︰生机系
考试日期(年月日)︰108.10.01
考试时限(分钟):100
试题 :
1. y = √(25-x^20 and y = -√(25-x^2) are solutions of dy/dx = -x/y on the in-
terval (-5,5).
(a) Draw the piecewise-defined function y = √(25-x^2), -5 < x < 0 (3%)
-√(25-x^2), 0 ≦ x < 5
(b) What are the two conditions to verify whether a function y(x) is the solu-
tion of a differential eq. y' = f(x,y). (4%)
(c) Explain why the function in (a) is not the solution of dy/dx = -x/y on the
interval according to (b). (3%)
Solve the following differential equations: 10% for each problem.
2. ln(y^x)y' = (x^2)y
3. yy' = 3xsec(2y)
4. 2cos(x+y) - 2xsin(x+y) - 2xsin(x+y)y' = 0
5. xy' = xcos(y/x) + y
6. 2y(1+x^2) + xy' = 0
7. y' + (x+y)^2 = 0
8. y' = y - y^6
9. y' = (xy+2y^2)/(x^2)
10. (x^2-y^2)dy = 2xydx

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