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Hi, i would like some help with his one

I have

[tex]\left\{\begin{aligned}y^{\prime\prime}+10y^{\prime}+25y = 0 \\

y(1) = 0 \\

y^{\prime}(1) = 2\end{aligned} [/tex]

So the first part is simple

The general solution is on the form

[tex]-5\pm\frac{\sqrt{10^2-4\cdot25}}{2}[/tex]

it's a double root

So we have

[tex] y = Ae^{-5t}+Bte^{-5t}[/tex]

And

[tex]y^{\prime} = -5Ae^{-5t} -5Bte^{-5t}[/tex]

[tex]-5e^{-5t}(A+Bt)[/tex]

And since t = 1

[tex]A=e^5~~ B=-e^5[/tex] works for the first condition but not for the second.

Hm, how do you do this?

I have

[tex]\left\{\begin{aligned}y^{\prime\prime}+10y^{\prime}+25y = 0 \\

y(1) = 0 \\

y^{\prime}(1) = 2\end{aligned} [/tex]

So the first part is simple

The general solution is on the form

[tex]-5\pm\frac{\sqrt{10^2-4\cdot25}}{2}[/tex]

it's a double root

So we have

[tex] y = Ae^{-5t}+Bte^{-5t}[/tex]

And

[tex]y^{\prime} = -5Ae^{-5t} -5Bte^{-5t}[/tex]

[tex]-5e^{-5t}(A+Bt)[/tex]

And since t = 1

[tex]A=e^5~~ B=-e^5[/tex] works for the first condition but not for the second.

Hm, how do you do this?

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