Integrating factor for xy dx + (2x^{2} + 3y^{2} -

Kathy Williams

Kathy Williams

Answered question

2021-12-20

Integrating factor for xydx+(2x2+3y220)dy=0

Answer & Explanation

Karen Robbins

Karen Robbins

Beginner2021-12-21Added 49 answers

Given:

xy dx +(2x2+3y220) dy =0 
m dx +n dy =0 
my=x nx=4x 
Since:

mynx 
So

 m(y)=nxmym=4xxxy=3y 
And:

 I.f=em(y) dy =e34 
I.f=e3lny=elny3 
I.f=y3

Andrew Reyes

Andrew Reyes

Beginner2021-12-22Added 24 answers

Equation is

 M(x,y) dx +N(x,y) dy =0 with M=xy,N=2x2+3y220
it is

 My=x Nx=4x,but NxMyM=3y

if only y is a factor, then the integrating factor is

 I.F.=e3lny=y3 

and generates the precise differential. 

dF(x,y)=P dx +Q dy =0, with P(x,y)=xy4,Q(x,y)=2x2y3+3y620y3
Solution 

F(x,y)=C 

by integrating the equation.

Fx=P 

wich gives 
F(x,y)=x2y42+G(y)

Using the

 Fy=Q

 G(y)=3y520y3 
i.e. G(y)=(12)y65y4+C

Hence F(x,y)=(y4)(x22+y25)=C.

RizerMix

RizerMix

Expert2021-12-29Added 656 answers

The equation is M(x,y)dx+N(x,y)dy=0 with M=xy,N=2x2+3y220. it is My... The solution F(x,y)=C is obtained integrating the eq.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?