Question

10yy'=x y(10)=4

Find the solution of the differential equation that satisfies the given initial condition.

Answer 1

Explanation:

10yy'=x

`10y(dy)/(dx) =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\(10y^2)/(2) =(x^2)/(2) +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=(60)/(2) =30\\10y^2=x^2+60\\10y^2-x^2=60`