How Do You Solve the Differential Equation dy/dt + (1/t)y = t*exp(-2t)?

[Eggmans]

Compute the general solution of the differential equation?

dy/dt+1/t y = t*exp(-2t)

y is outside 1/t


can't seem to get it

 

[AlephZero]

Find the integrating factor for the left hand side.

d/dt (some function * y) = ...

 

[HallsofIvy]

d(u(t)y)/dt= u(t)y'+ u'(t)y and you want that equal to u(t)y'+ (u(t)/t)y. That gives a simple separable equation for the integrating factor, u.

By the way, simpler than saying "y is outside 1/t" is to use parentheses: (1/t)y