## Calculus 8th Edition

As we are given that $y''+4y'+29y=0$, $y(0)=1$ and $y(\pi)=-1$ The roots are complex numbers such as $\alpha \pm i \beta$, thus the general solution is of the form $y=e^{\alpha x}[c_1cos(\beta x)+c_2sin(\beta x)]$ From the given values, $y(0)=1$ and $y(\pi)=-1$, we get $y(0)=1$ $$y(\pi)=-e^{-2\pi}\ne -1$$ This shows that the second boundary condition cannot be satisfied , hence the given problem does not have any solution.