I tried, no problem. > ex1 := (diff(f(x), x, x))*g(x)+(diff(f(x), x))*(diff(g(x), x)); > int(ex1, x); The result is d/dx(f(x))*g(x).

Dear Prof, It is really irritating that sometimes Maple does not understand your subs command. This is very likely due to Maple does not recognise out the part in the expression to be substituted. But I found a simple way to solve this situation: Just copy (in document mode) the part appearing as a total factor from Maple's (dsolve) output to subs command: >sol2 := subs(exp(-(zeta-sqrt(zeta^2-1))*omega[n]*t) = exp(-zeta*omega[n]*t)*(cos(sqrt(1-zeta^2)*omega[n]*t)+I*sin(sqrt(1-zeta^2)*omega[n]*t)), sol) >sol3 := subs(exp(-(zeta+sqrt(zeta^2-1))*omega[n]*t) = exp(-zeta*omega[n]*t)*(cos(sqrt(1-zeta^2)*omega[n]*t)-I*sin(sqrt(1-zeta^2)*omega[n]*t)), sol2) >sol4 := combine(sol3) sol4:=x(t)=(I*exp(-zeta*omega[n]*t)*omega[n]*zeta*x[0]*sin(sqrt(1-zeta^2)*omega[n]*t)+exp(-zeta*omega[n]*t)*omega[n]*sqrt(zeta^2-1)*x[0]*cos(sqrt(1-zeta^2)*omega[n]*t)+I*exp(-zeta*omega[n]*t)*v[0]*sin(sqrt(1-zeta^2)*omega[n]*t))/(sqrt(zeta^2-1)*omega[n]) Though Maple does not simplify imaginary radicals, I can do it by myself: sol5 := x(t) = exp(-zeta*omega[n]*t)*(zeta*x[0]+v[0]/omega[n])*sin(sqrt(1-zeta^2)*omega[n]*t)/sqrt(1-zeta^2)+exp(-zeta*omega[n]*t)*x[0]*cos(sqrt(1-zeta^2)*omega[n]*t) And I give sol5 a test: >odetest(sol5, {eqn1, x(0) = x[0], D(x)(0) = v[0]}) {0} So sol5 is the correct answer. slimriver

I found you squared Expr4-coeff(Expr4,G12)*G12 and coeff(Expr4,G12)*G12 to obtain Expr5. This results in the roots found belong to either Expr4 or Expr4-2*coeff(Expr4,G12)*G12. For example, when I substanciate the parameters, I got > V4 := Expr4-2*coeff(Expr4, G12)*G12; > V5 := Expr4; > simplify(subs(u1=sqrt(Vp),G11=10,G12=2,G22=1, G33=1,V4)); 0 > simplify(subs(u1 = sqrt(Vp), G11 = 10, G12 = 2, G22 = 1, G33 = 1, V5)); 192 a(x1, x2)^2 c(x1, x2) - --------------------------- 16 a(x1, x2) + 81 c(x1, x2) That verifies the root Vp does not belong to Expr4 and Expr1, but Expr4-2*coeff(Expr4, G12)*G12. The other root Vn belongs to Expr4 and Expr1. -slimriver-