MATH 2271 A -FAll 2022
Woldegebriel Assefa Woldegerima
September 28, 2022
Practice exercises
Part I: Put your last answer onl in teh space provided.
Q1 Consider the DE (1 − t)y (3) + 3x2 y 0 − y = sin x.
(i) Order of this DE is
(ii) Degree
(iii) Is this DE linear or non linear? Ans.
q
d2 y
dy 5
Q2 Consider the DE dx =
.
4 + dx
(i) Order of this DE is
(ii) Degree
(iii) Is this DE linear or non linear? Ans.
Part II: Workout questions. Show the required steps.
Q3 Verify that the given function is an explicit solution of the given DE, and determine the interval
of validity of solution.
√
(a) y(x) = x + 2 x + 5;
(b) y(x) = e3x cos(4x);
(y − x)y 0 = y − x + 2.
y 00 − 6y 0 + 25y = 0
Q4 Find all values of k so that y = ekx is a solution of 2y 00 + 5y 0 − 3y = 0.
Q5 Find C1 and C2 so that y = C1 cos(3x) + C2 sin(3x) is a solution teh BVP y” + 9y = 0,
0, y 0 (π) = 9
Q6 Solve
dy
=
(a) x dx
p
1 − y2.
dy
(b) (e2y − y) cos x dx
= ey sin 2x,
y(0) = 0.
1
y(0) =