Differential Equation Watch

Zagani
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#1
Report Thread starter 12 years ago
#1
I know I have to use Euler's Formual for this differential equation and I have done this bit fine... just by reducing it so it has constant coefficients with
y(t) instead of y(x) where x=e^t. just wanting to check if my method is actually correct and that ive got the right answer?!

x^2(d^2y/dx^2) + x(dy/dx) -4y =16

where y= dy/dx=0, when x=1

this gets down to:

d^2y/dt^2 - 4y=16
and complimentary function is then y=Ae^2t+Be^-2t

Particular Integral, y=k
therefore k=-4

so gen solution:
y=Ae^2t + Be^-2t - 4

y(x) = Ax^2 + B/(x^2) -4

y(1) = 0, so A+B=4
y'(1)=0, so 2A-2B=0
so, A=2, B=2

therefore final solution:

y(x) = 2x^2 + 2/(x^2) -4

thanks!
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