Solve y'' + 3y' - 10y=x(e^{x} + 1)

Isa Trevino

Isa Trevino

Answered question

2021-01-02

Solve y + 3y  10y=x(ex + 1)

Answer & Explanation

SabadisO

SabadisO

Skilled2021-01-03Added 108 answers

The auxiliary equation m2 + 3m  10=0
m=5, 2
the complimentary function yc=C1e5x + C2e2x
Now The P.I. of given differential equation is
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

 

Answer
y=yc + yp=C1e5x + C2e2x + e6(x + 76)  110(x + 710)

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