- #1

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## Homework Statement

Find x(t) given the following:

x(0)=2

[tex]dx/dt+4x=10e^{-2t}[/tex]

[tex]e^{4t}(dx/dt+4x)=10e^{-2t}e^{4t}[/tex]

[tex]d/dt(e^{4t}x)=10e^{2t}[/tex]

[tex]\int{d(e^{4t}x)}=\int{10e^{2t}dt}[/tex]

[tex]e^{4t}x+C=\int{10e^{2t}}[/tex]

[tex]e^{4t}x=\int{10e^{2t}}+C_1[/tex]

[tex]x(t)=\int{10e^{-2t}}+e^{-4t}C_1[/tex]

From here I get stuck. I know I can integrate it, but then I have another constant?