Question

the integrating factor of the differential equation y(ydx-xdy)+x^2(2ydx+2xdy)=0 is​

Answer 1

Answer:

Given, ydx−xdy=x2ydx

⇒1x2−1xy.dydx=1[dividing throughout by x2ydx]

⇒−1xy.dydx+1x2−1=0

⇒dydx−xyx2+xy=0

⇒dydx−yx+xy=0gt ⇒dydx+(x−1x)y=0

Which is a linear differential equation.

On compairing it with dydx+Py=Q, we get

P=(x−1x),Q=0

IF=e∫Pdx

=e∫(x−1x)dx

=ex2−logx

=ex2,e−logx

=1xex22

The general solution is y.1xe2/2=C

⇒y.1xex2/2=C