Internal problem ID [12770]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\alpha y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+alpha*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\sqrt {\alpha }\, x \right )+c_{2} \cos \left (\sqrt {\alpha }\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 28
DSolve[y''[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (\sqrt {a} x\right )+c_2 \sin \left (\sqrt {a} x\right ) \]