# Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of y(a)

#### AndreaA

Indicate why we can impose only n initial conditions on a solution of nth order linear differential equation.

A) Given the equation y'' + py'+ qy = 0
explain why the value of y''(a) is determined by the values of y(a) and y'(a).

B) Prove that the equation y'' - 2y' -5y =0
has the solution satisfying the conditions y(0) = 1, y'(0) = 0, and y''(0) = C
if and only if C = 5.

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#### matematikawan

Re: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of

A) Given the equation y'' + py'+ qy = 0
explain why the value of y''(a) is determined by the values of y(a) and y'(a).
The DE is linear so it must have a general solution which is a linear combination of two linearly independent solutions y1(x) and y2(x).

y(x)=c1y1(x) + c2y2(x) .

c1 and c2 can be determined uniquely from the given initial conditions. So the result can be deduce from here.

#### deluks917

Re: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of

Do you need to the dimension of the solution set to a second order system is two dimensional?