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

Isa Trevino 2021-01-02 Answered
Solve y + 3y  10y=x(ex + 1)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

SabadisO
Answered 2021-01-03 Author has 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)

Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more