Differential Equation with complex roots of CE !!!

[nirmal323]

Hi everyone,
If the general representation of second order differential equation is:
a*y''+b*y'+c*y=0;

I have the differential equation of the following form
y''-λ²* y=0. ................(1)
i.e. a=1, b=0 and c=-λ² ; where λ²=(α+i*β)
The characteristic equation of the eqn (1) is:
r²-λ²=0;
So that the roots of the characteristic equations are +λ and -λ.
Here the roots are a complex roots but not the conjugate. Can you please suggest me what will be the general solution for the equation (1) ?
I appreciate your help !!!

Thank you.
-Paudel



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[albbg]

Hi,
since the characteristic polinomial r²-λ²=0 has complex coefficients, roots will not be complex conjugated. The general solution will be:
y(x) = C1*exp(λ*x) + C2*exp(-λ*x)