problem with first-order nonlinear ordinary differential equation

i have problem to find the solution for :

i have tried the exact equation method :



thus M(x,y)=

and N(x,y)=

then deltaM/deltay=
and deltaN/deltax=

Since deltaM/deltay does not equal to deltaN/deltax, this imply that the eqution is not exact

thus, finding/searching for integrating factor :

1. 1/N(deltaM/deltay-deltaN/deltax)=
y cannot be eliminated . thus, this is a function of both x and y, not just x

2. 1/M(deltaN/deltax-deltaM/deltay)=

x cannot be eliminated . thus, this is a function of both x and y, not just y


thus i cannot find the integrating factor in order to solve the DE. where i'm gone wrong? can somebody point it out? i guess may be in algebra...

is there anyway for me to solve the de? please help me.... (Crying)

Your equation will be,



Now take y=vx

Then

Now substitute it in the above,

you will get,





Now integrate....


Result will be,

Quote:

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Originally Posted by kjchauhan

Your equation will be,



Now take y=vx

Then

Now substitute it in the above,

you will get,





Now integrate....


Result will be,

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I only got your's to work out if you start with (with the red term)