Applied Differential Equations (MT2043) Assignment 01
Submission Date: 01/03/2012
Instructor: Dr. Rashid Ali
Q1. Explain the following term:
1. Differential Equations
2. Classification or Types of the Differential Equations
3. Order and Degree of a Differential Equation
4. Linear Differential Equation
5. Separable Equations
6. Initial Value Problems
Q2. Give an example of an application/use of ordinary differential equation. (other than
Newton’s 2nd Law of motion).
Q3. Show that 1323 =+ xyx is an implicit solution of the differential equation
02 22 =++ yx
dx
dy
xy on the interval (0, 1).
Q4. Show that 125 2322 =− yxyx is an implicit solution of the DE 33 yxy
dx
dy
x=+ on the
interval (0, 2.5).
Q5. Show that 2
1
1
x
y
+
=is solution of the DE 024)1( 2
2
2=+++ y
dx
dy
x
dx
yd
x on every interval
(a, b) of the x-axis.
Q6. Eliminate the arbitrary constant A and B to obtain the differential equation whose general
solution is 1
22 =+ ByAx .
Ans. 0)( 2=
′
−
′
+
′′ yyyxyx
Q7. For the relation given by )cos( bnxay
+
=, form the corresponding differential equation.
Ans. 0
2=+
′′ yny (Here the arbitrary constants are a and b)
Q8. Obtain the DE for the 2-parameters family of solutions given by )(4)( 2hxaky −=− , h and
k are arbitrary constants.
Ans. 02
3
2
2=
⎟
⎠
⎞
⎜
⎝
⎛
+dx
dy
dx
yd
a
Q9. Solve 2
sinh :Hint
sinh2
cos yy
y
ee
y
ye
xx
dx
dy −
−
==
Ans. Cxxxye y++=− cossin
2
12
Q10. Solve 2
)14( ++= yx
dx
dy Hint: Put 4x + y +1 = t
Ans. Cx
yx +=
⎟
⎠
⎞
⎜
⎝
⎛++
−2
2
14
tan 1
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