Find the particular solution of the differential equation dy

Find the particular solution of the differential equation dy / dx = (x - 5) e -2y satisfying the initial condition y(5) = ln(5). y = Your answer should be a function of x.

dye^2y=(x-5)dx
==>e^2y /2= (x^2 /2 -5x)+c
==>e^2y=(x^2 -10x)+c
y(5)=ln5
==>25=(25-50)+c
==>c=50
==>e^2y=(x^2 -10x)+50
==>y=1/2 ln((x^2 -10x)+50)
=>y=ln((x^2 -10x)+50)