Solving Differential Equation: xy' + y = sqrt(x-1)

[Dell]

i just started a course in differential equations, and this question was in the homework that i got, I am not sure we learned how to solve it but maybe i am meant to know.

xy' + y = sqrt(x-1)

up until now all i have been able to solve is equations which i can bring to a form of dx/x +dy/y = 0 or something like that

because this question has 3 parts i haven't been able to get F(x)dx + F(y)dy=0

xy' + y = sqrt(x-1)

x*dy/dx + y =sqrt(x-1)

dy/y + x*dx = sqrt(x-1)*dx/y

dy/y = (sqrt(x-1)/y - x )dx

now i can't integrat this because on the right i have y as well as x and cannot get rid of it

 

[Bohrok]

Looks like you are familiar only with separable differential equations. Have you learned about integrating factors? That's what you need to solve this DE.