MATH 202 Final with Solution
American University of Beirut · Differential Equations · 1 page · with solution
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IPP Ma ere ey
FACULTY OF ART & SCIENCES, A.U.B.
Prof. N. H Mathematics 202
(1" semester, 1994-1995)
Time: 2 hou
1. Find the most general M(x, y) so that :
M(x, y)dx + (sin x cos y - xye” )dy = 0 is exact.
2. Solve the D.E.
(y-c¥sec?x)dx + (x-c%tan x)dy = 0,
3. Solve the IVP
y +3x''y = xy’; y(1) = 2.
4. Given y'(x) = (x-1) is a solution for
xy” +(1-x)y’+y = 0, x>0,
obtain a representation for the second solution.
5. Find the general solution
x2y”"+2xy’-2y = 6x"+ 3x.
6. Apply the method for Frobenius to solve
x(1-x)y”-3y’+2y = 0. :
7. Use the substitution y = x? u(x) to solve
y+k*x’y =0
8. Solve the IVP
1
y'ty — fy(v) sin(t— v)dv=—sint; y(0)=1
0
9. Solve the IVP
y’ty = 8(t-2m)-S(t—-m); (0) =0, YO=1.
10. Solve : y”’-l2y”+27y’+40y = 0.
February, 1995
(Closed book)
43