allisonmorency allisonmorency
  • 01-02-2017
  • Mathematics
contestada

Find the solution of the given initial value problem. y'-y=11te^2t, y(0)=1

Respuesta :

LammettHash
LammettHash LammettHash
  • 01-02-2017
[tex]y'-y=11te^{2t}[/tex]
[tex]e^{-t}y'-e^{-t}y=11te^t[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dt}\left[e^{-t}y\right]=11te^t[/tex]
[tex]e^{-t}y=11\displaystyle\int te^t\,\mathrm dt[/tex]
[tex]e^{-t}y=11e^t(t-1)+C[/tex]

Since [tex]y(0)=1[/tex], you have

[tex]1=11(-1)+C\implies C=12[/tex]

and so

[tex]e^{-t}y=11e^t(t-1)+12[/tex]
[tex]y=11e^{2t}(t-2)+12e^t[/tex]
Answer Link

Otras preguntas

Credit for the first synthesis of an organic compound from an inorganic precursor is usually given to ___.
A molecular biologist measures the mass of Cofactor A in an average yeast cell. The mass is 77.91pg. What is the total mass in micrograms of Cofactor A in an av
The population in your state has nearly doubled in the last fifty years. People now live in places that were once farms or forests. Land has been cleared to mak
How does free housing reduce poverty
An online music club sells compact discs for $13.95 each plus $1.95 shipping and handling per order. If Maria's total bill was $85.65, how many compact discs di
-3a-3=2n+3p solve for a
. A _______ relationship exists between an employee and a supervisor.
What is the significance of the main verbs in the meaning of a passage?
Hkw do you solve 1/3(6x-9)=7-2x?
Simplify 6a + 10a + 3a