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## Homework Statement

[tex]y'' - 4y = 0[/tex] when y = 1, y' = -1, x = 0

**2. The attempt at a solution**

[tex]y'' - 4y = 0[/tex]

[tex]m^2 - 4 = 0[/tex]

[tex]m = 2, m = -2[/tex]

Substituting: [tex]y = 1, x = 0[/tex]

[tex]1 = C1 + C2[/tex]

[tex]C1 = -C2 + 1[/tex]

Substituting: [tex]y' = -1, x = 0[/tex]

[tex]-1 -C2 + 1 + C2[/tex]

[tex]C2 = C2[/tex]

Therefore: [tex]y = -C2e^2^x + C2e^-^2^x[/tex]

Obviously I went wrong with my substitutions... Can I get a hint?