Make and solve the given equation d^{3} frac{y}{dx^{3}} - d^{2} frac{y}{dx^{2}}=2x + 3

Tolnaio 2020-12-15 Answered
Make and solve the given equation d3 ydx3  d2 ydx2=2x + 3
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Expert Answer

hajavaF
Answered 2020-12-16 Author has 90 answers

Given d3 ydx3  d2 ydx2=2x + 3
The above equation can be written as (D3  D2)y=2x + 3
Now the auxiliary equation is m3  m2=0
which gives m=0, 0, 1
Hence the complimentary function is C.F.=C1 + C2x + c3ex
Now we need to find the Particular Integral
yp=1D2 + 3D  10x(xx + 1)=1(D + 5)(D  2)xex + 1
=ex1(D + 1 + 5)(D + 1  2)x + 1(D + 5)(D  2)x
=ex1(D + 6)(D  1)x + 1(D + 5)(D  2)x
=ex16(1 + D6)(1  D)x + 110(1 + D5)(1  D2)x
= ex6(1 + D6)1(1  D)1x  110(1  D5)1(1  D2)1x
=  ex6(1 + D6 + )(1 + D + D2)x  110(1 + D5 )(1 + D2 + )x
=  ex6(x + 1 + 16)  110(x + 15 + 12)
=  ex6(x + 76)  110(x + 710)
Hence the general solution is
y=yc + yp=C1e5x + C2e2x ± e6(x + 76)  110(x + 710)

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Jeffrey Jordon
Answered 2021-11-03 Author has 2313 answers

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