MATH 202 Final, Fall 1996
American University of Beirut · Differential Equations · 1 page
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Prof. N. Haidar FACULTY OF ARTS & SCIENCES , A. U. Bb.
Sec. 1&2 Math 202 Feb. 1, 1997
(1-st Semester , 1996-1997)
Time: 2 hours ‘ FINAL EXAM (closed book)
6) I. Solve the DE
(x+sinx-+siny)dx + cosydy =0.
® UI. Determine the valucs of A for which the BVP
y+ ay =0 5 y= 0, y(n = 0,
has nontrivial solutions .
© IV. Determine the maximal domain of uniqueness for the solution to the IVP.
y” +inx ye? y = tanx ; y"Q)= yQ) = y(2) =0.
® V. Solve the DE
(x-3)7y"- 3(x-3) yo + 4y =x.
@ VIL. Apply the method of Frobenius to find the gencral solution to the DE
i
(1+x) x? y” -(142x) xy’ + 42x) y = 0,
in the neighborhood of its x =-1 singularity .
® VILSolve the nonhomogencous Bessel’s DE ,
12
x yh exy t (x -u)y = x? , x>0.
® UX.Solve the IVP ;
{b,O0St<a
yty= (@) 3 yO=t, y= 0,M=4 pa>b>0.
Lab,ast
® IX. Solve the system of integral equations
f ys 2a- f (t-u) y(u) du + { z(v) dv
{
L 2=-2-4[' yw) dv + 3 f (ed ae dt
z 0 y 0
for y(t) only.