Solve[x^2+x+1==0,x]

x^2+x+1==0/.%//Simplify

DSolve[y''[x]+y[x]==Exp[x],y,x]

y''[x]+y[x]==Exp[x]/.First[%]//Simplify

soln=DSolve[y''[x]-Exp[x]y[x]==0,y,x]

y''[x]-Exp[x]y[x]==0/.First[soln]//Simplify

y''[x]-Exp[x]y[x]==0/.First[soln]//FullSimplify