Internal problem ID [5207]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 59
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+10 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = \pi , y^{\prime }\relax (0) = \pi ^{2}] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)+10*y(x)=0,y(0) = Pi, D(y)(0) = Pi^2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\pi \left (\pi \sqrt {10}\, \sin \left (\sqrt {10}\, x \right )+10 \cos \left (\sqrt {10}\, x \right )\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 33
DSolve[{y''[x]+10*y[x]==0,{y[0]==Pi,y'[0]==Pi^2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\pi ^2 \sin \left (\sqrt {10} x\right )}{\sqrt {10}}+\pi \cos \left (\sqrt {10} x\right ) \\ \end{align*}