Get Study Tools
Skilled2021-01-26Added 109 answers
Step 1Given that(d2x)(dt2)+(d2y)(dt2)=t2…(A)(d2x)(dt2)−(d2y)(dt2)=4t…(B)x(0)=5,x′(0)=0,y(0)=0,y′(0)=0adding equation( A) and (B)⇒2(d2x)(dt2)=(t2+4t)(d2x)(dt2)=(t2+4t)2(d2x)(dt2)=(t2)2+2tStep 2taking Laplace transform on both sides,s2X(s)−sx(0)−x′(0)=12+2s2+2s2s2X(s)−5s=1(s3)+2s2s2X(s)=(1+2s+5s4)s5X(s)=1s5+2s4+5staking Inverse Laplace transformx(t)=t44!+(2t3)3!+5u(t)Step 3u(t)=1,t≥0=0,t<0∴x(t)=(t4)24+(t3)3+5 for t≥0And Subtracting equation (B) from (A)⇒2(d2y)(dt2)=t2−4t(d2y)(dt2)=(t2−4t)2=(t2)2−2tTaking ILTs2Y(s)−sy(0)−y′(0)=122s3−2s2s2Y(s)=1(s3)−2(s2)=(1−2s)s3Y(s)=(1−2s)s5Step 4Y(s)=1s5−2s(s5)Y(s)=1s5−2(s4)Taking Inverse Laplace Transformy(t)=(t4)4!−(2t3)3!=(t4)24−(t3)3
Do you have a similar question?
Recalculate according to your conditions!
Ask your question. Get an expert answer.
Let our experts help you. Answer in as fast as 15 minutes.
Didn't find what you were looking for?
Connect with us
Get Plainmath App
Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus
Cyprus reg.number: ΗΕ 419361
E-mail us: email@example.com
Our Service is useful for:
Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.
2023 Plainmath. All rights reserved