- #1
Naeem
- 194
- 0
Hi,
Q 1. ( e ^ y/x - y/x e ^ y/x + 1 / 1 + x^2 ) dx + e ^ y/x dy = 0
Ans. I know its Homogeneous sub, y = ux,
then, dy / dx = u dx + x du
I did this, and got to the point,
e^u dx + 1 / ( 1 + x^2) dx + x. e^u du = 0
How can we separate this now?
Q 2. y dx + ( 2x - y e^y ) dy = 0
I think we can use exactness, here
M = y
My = 1
N = 2x - y e^y
Nx = 2
Not exact,
so,
Integrating Factor would be : e ^ Integral My - Nx / N
Is this right. Integrating factor is getting to complicated to multiply the eqn, with. Any better way of doing this.
Q 3. ( 2x + tany) dx + ( x - x^2 tany ) dy = 0
I think here too, exactness, may be used, but any better way, if possible.
Q 1. ( e ^ y/x - y/x e ^ y/x + 1 / 1 + x^2 ) dx + e ^ y/x dy = 0
Ans. I know its Homogeneous sub, y = ux,
then, dy / dx = u dx + x du
I did this, and got to the point,
e^u dx + 1 / ( 1 + x^2) dx + x. e^u du = 0
How can we separate this now?
Q 2. y dx + ( 2x - y e^y ) dy = 0
I think we can use exactness, here
M = y
My = 1
N = 2x - y e^y
Nx = 2
Not exact,
so,
Integrating Factor would be : e ^ Integral My - Nx / N
Is this right. Integrating factor is getting to complicated to multiply the eqn, with. Any better way of doing this.
Q 3. ( 2x + tany) dx + ( x - x^2 tany ) dy = 0
I think here too, exactness, may be used, but any better way, if possible.