How To Solve A Second Order Differential Equation In Fortran. Another python package that solves different equations is gekko. $$\mathbf{y}'' + a\mathbf{y}'= \mathbf{b} + \mathbf{a}\mathbf{y}$$ with initial conditions $\mathbf{y} = \mathbf{y}' = \mathbf{0} $, $\mathbf{a} \in \mathbb{r}^{n \times n}$, $\mathbf{y} \in \mathbb{r}^{n }$ and $a$ is a scaler.
U ( x) = e x is clearly one solution. This is the case for boundary value problems, such as the equations for vibrating systems, or for the conduction of heat. For instance, in the following differential equation:
