Question

ADVANCE ENGINEERING MATHEMATICS HELP!!!?

Answer 1

1)y'-xy=1-x

The given first order D.E in the form of leibnitz's linear equation  

So the integrating factor (IF) is  

Now compare the given  D.E with leibnitz's linear equation p =-x  g = 1- x

IF = 

     =

Now the solution for the given equation is 

                  = 

From Gaussian integral 

Now 

Let x² / 2 = t

x² =2t

2x.dx=2dt

dx = dt / x

so                  

 

So the solution for given D.E is