- #1
James889
- 192
- 1
Hi,
I have the equation [tex]y'' +4y = t~sin(t)[/tex]
i know that you usually guess the solution by substituting y for a polynomial (or whatever the form of the right side is).
But i want to do this by using the exponential function exp.
so, set y to equal [tex]te^{it}[/tex]
chain rule:[tex]y^{\prime} = 1 \cdot e^{it} +t \cdot ie^{it} = e^{it} +tie^{it}[/tex]
[tex] y^{\prime\prime} = ie^{it} + ie^{it} \cdot ti + ie^{it} = 2ie^{it} \cdot ti + ie^{it}[/tex]
hm, is this really correct?
and how would you proceed?
I have the equation [tex]y'' +4y = t~sin(t)[/tex]
i know that you usually guess the solution by substituting y for a polynomial (or whatever the form of the right side is).
But i want to do this by using the exponential function exp.
so, set y to equal [tex]te^{it}[/tex]
chain rule:[tex]y^{\prime} = 1 \cdot e^{it} +t \cdot ie^{it} = e^{it} +tie^{it}[/tex]
[tex] y^{\prime\prime} = ie^{it} + ie^{it} \cdot ti + ie^{it} = 2ie^{it} \cdot ti + ie^{it}[/tex]
hm, is this really correct?
and how would you proceed?