Home
Class 12
MATHS
Solve x (dy)/(dx)sin(y/x)+x-ysin(y/x)=0 ...

Solve `x (dy)/(dx)sin(y/x)+x-ysin(y/x)=0` given `y(1)=pi/2`

Text Solution

Verified by Experts

`x(dy/dx)sin(y/x)+x-ysin(y/x) = 0`
Dividing given equation with `xsin(y/x)`
`=>dy/dx+1/sin(y/x)-y/x = 0`
Let `y/x = v`
Then, `y = vx =>dy/dx = v+x(dv)/dx`
So, given equation becomes,
`=>v+x(dv)/dx+1/sinv-v = 0`
`=> x(dv)/dx = -1/sinv`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

(xe^(y/x)-ysin(y/x))dx+xsin(y/x)dy=0

(xe^(y/x)-ysin(y/x))dx+xsin(y/x)dy=0

solve x(dy)/(dx) - y + x sin ((y)/(x)) = 0

Show that the differential equation x(dy)/(dx)sin(y/x)+x-ysin(y/x)=0 is homogenous. Find the particular solution of this differential equation, given that x=1 when y=pi/2 .

(dy)/(dx)=ysin2x given, y(0)=1

Solve x(dy)/(dx)=y+x tan(y/x) , given that y=(pi)/(2) , when x=1.

Solve: (dy)/(dx)=ysin2x it being given that y(0)=1.

Solve xsin(y/x)dy=(ysin(y/x)-x)dx .

Solve xsin(y/x)dy=(ysin(y/x)-x)dx .