Find a particle solution for differential equation in a form [tex]y_p=a\cdot e^x,[/tex] where a is unknown coefficient.
If [tex]y_p=a\cdot e^x,[/tex] then
- [tex]y_p'=(a\cdot e^x)'=a\cdot e^x,[/tex]
- [tex]y_p''=(a\cdot e^x)'=a\cdot e^x.[/tex]
Substitute these data into the differential equation:
[tex]a\cdot e^x-5\cdot a\cdot e^x+5\cdot a\cdot e^x=3e^x,\\ \\a\cdot e^x=3e^x,\\ \\a=3.[/tex]
Thereofre, the particle solution for differential equation is
[tex]y_p=3e^x.[/tex]
