Ex 9.4, 8 - Chapter 9 Class 12 Differential Equations

Last updated at May 26, 2023 by Teachoo

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Ex 9.4, 8
show that the given differential equation is homogeneous and solve each of them.
+ =0
Step 1: Find
= y x sin
Step 2. Put = F (x, y) and find F( x, y)
F(x, y) = sin
F( x, y) = sin = sin = F(x, y)
= ( , )
F (x, y) is a homogenous function of degree 0 .
So the differential equation is homogenous
Step 3 : Let y = vx Solving = - sin
Putting y = vx
Diff w.r.t.x
= x + v
= x + v
Putting value of = 2 + 2 2 + and y = vx in (1)
= y x sin
v + = sin
v + = sin v
= v sin v v
= sin
= sin
=
Integrating both sides
=
=
log cot = log + log
log cot + log = log
log ( cot ) = log
x (cosec v cot v) = C
x 1 sin cos sin = C
x (1 cos ) sin = C
x(1 cos v) = C sin v
Putting value of v =
x = C sin

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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