Pure Mathematics

1)
x = 1/t
...
x^5 d^2z/dx^2 + (2x^4 - 5x^3) dz/dx +4xz = 6x +3 can be reduced to....

d^2z/dt^2 + 5 dz/dt + 4z = 3t+6

2)
use the substitution y=x^2 to show that...
x d^2x/dt^2 + (dx/dt)^2 + 5x(dx/dt) + 3x^2 = sin2t + 3cos2t

can be converted to

d^2y/dt^2 + 5dx/dt + 6y = 2sin2t + 6cos2t

hence solce for x in terms of t

1. 👍 0
2. 👎 0
3. 👁 85
1. assume a solution in the form of

y=AsinBt+CcosDt then
y'= BAcosBt -CDsinDt
y"=-B^2 A sinBT + CD^2 cosDt

put those in the equation..
-B^2 A sinBT + CD^2 cosDt +5BAcosBt -6CDsinDt +6AsinBt+6CcosDt =2sin2t + 6cos2t

work with the sin terms first:

-B^2 A sinBT -6CDsinDt +6AsinBt =2sin2t
It is clear B=D=2
-4A-12C+12=2 **1
then the cosine terms...
CD^2 cosDt +5BAcosBt +6CcosDt = + 6cos2t
again, D=B=2
4C+10A+6C=6***2
now, you have two equations, two unknowns, solve for A and C. ...and you have the solution

1. 👍 0
2. 👎 0
2. i worked that part out and got my terms but then noticed that there's a x'term mixed in with the y terms...the ones that are the real problem though are 1 and part a of number 2

1. 👍 0
2. 👎 0

Similar Questions

1. math home work

solve the following equations for the variable x 4x=y xyz=t 4xz=P y=xtz 3.5tpx=R

asked by sherri on October 6, 2008
2. Math

I was wondering if I solved these problems right? Simplify the following: 3xy^2 4xz ______ + ______ = 7xyz 2y 3x _____ 5 2(x-1) 3(x^2-4) ______ * ________ = 6(x-2) 4(x+2) 5x-5 ______ 20 x^2-x-6 3(x^2-4) ________ / __________ =

asked by Sara on June 13, 2011

More Similar Questions