Find the solution to initial value problem d2ydt220dydt100y0

Find the solution to initial value problem

d^2y/dt^2-20dy/dt+100y=0

y(0)=7, y\'(0)=9

It is a linear homogeneous recurrence

So we assume solution of the form

y=exp(kt)

Substituting gives

k^2-20k+100=0

k=10 ie repeated roots

So general solution is

y(t)=e^{10t}(A+Bt)

y(0)=A=7

y\'(t)=10e^{10t}(A+Bt)+Be^{10t}

y\'(0)=10A+B=9=70+B

B=-61

y(t)=e^{10t}(7-61t)

$Find the solution to initial value problem d^2y/dt^2-20dy/dt+100y=0 y(0)=7, y\'(0)=9SolutionIt is a linear homogeneous recurrence So we assume solution of the f$

Find the solution to initial value problem d2ydt220dydt100y0

Solution

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