Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Model Papers
0 votes

Solve the differential equation $ y.e^{\large\frac{x}{y}} dx=(x.e^{\large\frac{x}{y}}+y^2)dy ; y \neq 0$

Can you answer this question?

1 Answer

0 votes
  • A differential equation of the form $\large\frac{dy}{dx }$$= F(x,y)$ is said to be homogenous if $F(x,y)$ is a homogenous function of degree zero.
  • To solve this type of equations substitute $y = vx$ and $\large\frac{dy}{dx }$$= v + x\large\frac{dv}{dx}$
Step 1:
This can be written as
$\large\frac{dx}{dy}=\frac{xe^{\Large x/y}+y^2}{ye^{\Large x/y}}$
Step 2:
Clearly this is a homogeneous differential equation .
Hence put $x=vy$
$\therefore v+y\large\frac{dv}{dy}=\frac{vye^v+y^2}{ye^v}$
$\Rightarrow \large\frac{ ve^v+y}{e^v}$
$\Rightarrow y\large\frac{dv}{dy}=\frac{ve^v+y}{e^v}$$-v$
Step 3:
Now separating the variables we get,
On integrating we get
$\int e^vdv=\int dy$
(i.e) $e^v=y+c$
Substituting for $v=\large\frac{x}{y}$ we get,
This is the required solution.
answered Nov 7, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App