Question

35. Show that the differential equation xdy/dxsin(y/x)+ X-(y/x)=0
is homogenous .
Find the particular solution of this differential equation given that x = 1 when y=π/2
​

Answer 1

Answer:

Devide this equation by x(dy/dx).. You will find this equation is homogeneous

Step-by-step explanation:

Now assume that y/x=θ

therefore y=θx

now diffrentiate it you will get ,

dy/dx=θ+dθ/dx

now put that value in homogeneous equation you will get ,

θ+dθ/dx=-sin(y/x)/1-y/x

now solve that equation and integrate it you will get that x=1 when y=π/2