Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients...

Consider the differential equation,

L[y] = y'' + p(t)y' + q(t)y = 0, (1)

whose coefficients p and q are continuous on some open interval I. Choose some point t₀ in I. Let y₁ be the solution of equation (1) that also satisfies the initial conditions

y(t₀) = 1,

y'(t₀) = 0,

and let y₂ be the solution of equation (1) that satisfies the initial conditions

y(t₀) = 0,

y'(t₀) = 1.

Then y₁ and y₂ form a fundamental set of solutions of equation (1).

Find the fundamental set of solutions specified by the theorem above for the given differential equation and initial point.

y'' + 8y' − 9y = 0,

t₀ = 0

y₁(t)	=
y₂(t)	=

Expert Solution

I hope it helps. Please feel free to revert back with further queries.

Colby Messinger answered 5 months ago

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