Assignment of Applied Mathematics III
1. Find a general solution of the following homogeneous differential equation of the
second order.
a) 𝑦′′ + 3𝑦′ + 4𝑦 = 0
b) 𝑥 2 𝑦′′ − 4𝑥𝑦′ + 6𝑦 = 0
2. Find particular solution of the following differential equation of the second order.
a) 𝑦′′ + 2𝑦′ + 𝑦 = 0
𝑦(0) = 3 , 𝑦′ (0) = 0
b) 𝑥 2 𝑦′′ − 5𝑥𝑦′ + 8𝑦 = 0
𝑦(1) = 5 , 𝑦′(1) = 18
3. Find general solution of the following non homogeneous differential equation of
the 2nd Order.
a). 𝑦 ′′ − 2𝑦 ′ + 5𝑦 = 𝑒 2𝑥 sin 𝑥 b). 𝑦 ′′ − 4𝑦 ′ − 5𝑦 = 𝑥𝑒 −𝑥
c). 𝑥 2 𝑦’’ − 𝑥𝑦’ − 3𝑦 = 𝑥 2 + 𝑙𝑛𝑥
4. Find the work done by the force field:
(a ) F  x 2 yi  xj as a particle moves from (1,0) to (6,5) along the straight line joining
these points.
5. Evaluate the integrals.
2
2
C x y dx  2 y xdy : where C consists of the circle x  y  1 from (1,0) to
(0,1) and the line segment from (0,1)to (4,3).