Answer
No solution.
Work Step by Step
$y''+4y'+29y=0$, $y(0)=1$ and $y(\pi)=-1$
Roots are complex numbers: $\alpha \pm i \beta$, thus the
General solution: $y=e^{\alpha x}[c_1cos(\beta x)+c_2sin(\beta x)]$
Plug in the given values: $y(0)=1$ and $y(\pi)=-1$
Hence, $y(0)=1$
$y(\pi)=-e^{-2\pi}\ne -1$
Since, the second boundary condition cannot be satisfied and the given problem does not have a solution.
