Linear Differential Equations (on Paul's online notes) : I don't understand how you get from this step: u(t)*dy/dt + u'(t)y = u(t)g(t)
to This step: u(t)dy/dt + u'(t)y = [ u(t)*y(t)]
where does the y(t) come from on the left hand side?

Question

Linear Differential Equations (on Paul's online notes) : I don't understand how you get from this step: u(t)*dy/dt + u'(t)y = u(t)g(t) 
to This step: u(t)dy/dt + u'(t)y = [ u(t)*y(t)] 
where does the y(t) come from on the left hand side?

shubhamsrg · Answer

well i dont know how we got y(t) but this liner differential eqn 
u(t)*dy/dt + u'(t)y = u(t)g(t) 
 can be solved easily using integrating factor..

anonymous · Answer

okay, thank you. How is u(t)dy/dt + u'(t)y = [ u(t) * y(t)]? I know it is the product rule but I don't understand the process

shubhamsrg · Answer

just as i said,,i dont know how they got y(t) in there,,seems wrong to me,,i might be wrong saying that..but,,what i am saying is your original problem can be easily computed by the use of integrating factor..if you know what that is..which i guess you must be knowing..

anonymous · Answer

yes, thanks!