Differential equations - separable
dy/dx=(1+lnx)y and if y=1 when x=1, then y=?

Question

Differential equations - separable 
dy/dx=(1+lnx)y and if y=1 when x=1, then y=?

precal · Answer

when I separate them I get
dy/y=(1+lnx)dx
I don't know how to integrate the right side

nincompoop · Answer

As separate if want

precal · Answer

not sure I understand your statement

nincompoop · Answer

As. Separate equation

nincompoop · Answer

Lorry my tablet is not responding well

precal · Answer

that's ok, I am on my ipad.  I am having issues as well

precal · Answer

what is the Q for?  Boy is this website different

superdavesuper · Answer

$$\frac{ 1 }{y }dy = \left( 1 + lnx \right)dx = dx + lnx dx$$

so integrating both sides

$$\int\limits_{}^{}\frac{ dy}{ y } = \int\limits_{}^{}dx +\int\limits_{}^{}\ln(x)dx$$

u can continue from here. good luck :)

precal · Answer

thanks

precal · Answer

This is an integration by parts problem. No wonder I forgot how to do it.