75.22.6 problem 711

Internal problem ID [17185]
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 ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 711
Date solved : Tuesday, January 28, 2025 at 09:56:30 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=\alpha \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \sin \left (x \right ) \alpha \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 9

DSolve[{D[y[x],{x,2}]+y[x]==0,{y[0]==0,y[Pi/2]==\[Alpha]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \alpha \sin (x) \]