Internal problem ID [15455]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 17. Boundary value problems. Exercises page
163
Problem number: 711.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 0, y \left (\frac {\pi }{2}\right ) = \alpha \right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve([diff(y(x),x$2)+y(x)=0,y(0) = 0, y(1/2*Pi) = alpha],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) \alpha \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 9
DSolve[{y''[x]+y[x]==0,{y[0]==0,y[Pi/2]==\[Alpha]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \alpha \sin (x) \]