Convert the equation into a first-order linear differential equation system with an appropriate transformation of variables.y"+4y'+3y=x^2

Sinead Mcgee 2021-09-06 Answered

Convert the equation into a first-order linear differential equation system with an appropriate transformation of variables.
y"+4y+3y=x2

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doplovif
Answered 2021-09-07 Author has 71 answers

y"+4y+3y=x2(1)
Let y=u1(2)
y=u2(3)
From (2) , y=u1u1=u2
From (3) , yu2
u2=y
From (1) , yx24y3y
=x24u23u1
u2=3u14u2+x2
Hence u1=u2
u2=3u14u2+x2
[u1u2]=[0134][u1u2]+[0x2]
v=Av+b
Where u=[u1u2],A=[0134],b=[0x2]

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