u+xu'=ulnu

Du/u of separation variable (lnu-1) = dx/x.

d(lnu- 1)/(lnu- 1)= dx/x

ln|lnu- 1|=ln|x|+C

lnu- 1=Cx

Y=e when x= 1? , so u=e? Substitute the above formula to get C= 1.

So lnu=x+ 1.

ln(y/x)=lny-lnx=x+ 1

lny=lnx+x+ 1

y=xe^(x+ 1)

Many kinematics and dynamics problems involving variable forces in physics, such as falling bodies with air resistance as speed function, can be solved by differential equations. In addition, differential equations have applications in chemistry, engineering, economics and demography.

The research on differential equations in the field of mathematics focuses on several different aspects, but most of them are related to the solutions of differential equations. Only a few simple differential equations can be solved analytically. However, even if the analytical solution is not found, some properties of the solution can still be confirmed. When the analytical solution cannot be obtained, the numerical solution can be found by means of numerical analysis and computer. ?