Transform the given initial value problem into an initial value problem for two first-order quationsu"+0.25u'+4u=2cos(3t), u(0)= 1, u'(0)= -2

permaneceerc

permaneceerc

Answered question

2021-03-02

Transform the given initial value problem into an initial value problem for two first-order quations u"+0.25u+4u=2cos(3t), u(0)=1,u(0)=2

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-03-03Added 98 answers

Let u=x1 and u=x2
x1=u and x2=u"
or x1=x2 and x2=u"
:u"+0.25u+4u=2cos(3t)
u"=2cos(3t)0.25u4u (:u=x1,u=x2)
x2=2cos(3t)0.25x24x1
x1=x2
x2=2cos(3t)4x10.25x2
or
x1=0x1+x2
x2=4x10.25x2+2cos(3t)
:u(0)=1x1(0)=1 (because u=x1)
u(0)=2x2(0)=2 (because u=x2)
Hence the initial value problem for two first-order quations is
x1=0x1+1x2
x2=4x10.25x2+2cos(3t)
x1(0)=1, x2(0)=2

Jeffrey Jordon

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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