calc quadratic?!?!?

deadrabit · #1 $Old$ August 26th, 2008, 05:47 AM

heyya, got an exam in a few days... just going over old exam papers and found.

x = 1-e^-t (sin3t + 3cos3t)
dx/dt = 10e^-t sin(3t)
d^x/dt^2 = e^-t (3cos3t - sin3t)

show that: d2x/dt2 + 2dx/dt + 10x = 10
got a Latex image of it because i know formulea are hard to read like that^^

anyway... never seen a calculus question like it (also i did the working for dx/dt and d2x/dt2 so maybe errors) and i was hoping someone could point me in the right direction.

> maybe a name used, if it were in a textbook what would the title be
> any good resources from mathsworld or wikibooks math etc... on this type of question
> or if you have the time specific help with this question =]

thanks for any help
Dead.Rabit

p.s. first post... im new here XD

Simplicity · #2 $Old$ August 26th, 2008, 06:12 AM

This is Second order differential equation. Have a read on these sites:

Second Order Differential Equations - Generalities
Homogeneous 2nd-order differential equations
Notes on 2nd order d.e.'s
PlanetMath: second order linear differential equation with constant coefficients

Laurent · #3 $Old$ August 27th, 2008, 11:49 AM

Actually, you don't need to know anything about differential equations.

You computed $\frac{dx}{dt}$ and $\frac{d^2x}{dt^2}$ (warning: you forgot a factor 10 in the latter). The whole you are asked to do now is to compute the sum $\frac{d^2x}{dt^2}+2\frac{dx}{dt}+10x$ and to check that you get 10. Which is the case indeed.