75.22.6 problem 711

Internal problem ID [17106]
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 : Thursday, March 13, 2025 at 09:16:11 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*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 8

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
ic:=y(0) = 0, y(1/2*Pi) = alpha; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.056 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, y(pi/2): alpha} 
dsolve(ode,func=y(x),ics=ics)
 

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