Log(dy/dx) = 3x+ 4y

Question

Solve the differential equation

 

Answer 1

Assuming that the logarithm's base is e (if not so, YOU can make a suitable correction):

dy/dx = e^3x+4y

dy = e^3xe^4ydx

...typo corrected

 

e^-4ydy = e^3xdx

 

Now you have separated variables & the antidifferentiation, etc. is easy from here on.