Simplify to obtain the form

in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer


Let u=a+ib and v=a-ib, then x=Ce^ut+De^vt.

x'=uCe^ut+vDe^vt; x"=u^2Ce^ut+v^2De^vt.

u+v=2a and uv=a^2+b^2. (x-r1)(x-r2)=x^2-(r1+r2)x+r1r2 so if we let r1=u and r2=v we have x^2-2ax+a^2+b^2=(x-u)(x-v).

x"-2ax'+(a^2+b^2)x=0 has the general solution x=Ce^ut+De^vt as can be seen by substituting for x", x' and x, a and b:


by Top Rated User (1.0m points)

Related questions

1 answer
1 answer
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,067 questions
96,685 answers
24,366 users