`y^2dx+(x^2+x y+y^2)dy=0` – InterviewSolution

InterviewSolution

1.	`y^2dx+(x^2+x y+y^2)dy=0`
Answer» Correct Answer - `log\|y/(y+x)\|+log\|x\|+x/(y+x)=C` `int1/(v(v+1)^(2))dv=-int1/xdx`. Let `1/(v(v+1))^(2)=A/v+B/(v+1)+C/(v+1)^(2)` This gives A=1, B`=-1` and `C=-1`.

Discussion

No Comment Found

Related InterviewSolutions

Show that the differential equation `2y e^(x/y) dx+(y-2x e^(x y)`) `dy=0`ishomogeneous. Find the particular solution of this differential equation,given that `x=0`when `y=1.`
Find the particular solution, satisfying the givencondition, for the following differential equation:`(dy)/(dx)-y/x+cos e c (y/x)=0; y=0`when `x=1`
Find the particular solution of the differentialequation `(3x y+y^2)dx+(x^2=x y)dy=0;for x=1, y=1.`
Find the particular solution of the differential equation `(xe^(y//x)+y)dx=xdy`, given that `y(1)=0`.
Find the particular solution of the differential equation `xe^(y/x)-y+xdy/dx=0,` given that `y(e)=0.`
`x(dy)/(dx)-y+xsin(y/x)=0`
Find the particular solution of the differential equation `(dy)/(dx)=(y(2y-x))/(x(2y+x))`,given that `y=1` when `x=1`.
Find the particular solution of the differential equation `{xsin^(2)(y/x)-y}dx+xdy=0`, it being given that `y=pi/4` when `x=1`.
Solve : `(x+y)dy+(y-2x)dx=0`
`(x-y)dy-(x+y)dx=0`