69.22.9 problem 714

Internal problem ID [18475]
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 : 714
Date solved : Thursday, October 02, 2025 at 03:13:59 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\mathrm e}^{\alpha } \\ y^{\prime }\left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 6

ode:=diff(diff(y(x),x),x)+alpha*diff(y(x),x) = 0; 
ic:=[y(0) = exp(alpha), D(y)(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{\alpha } \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 8

ode=D[y[x],{x,2}]+\[Alpha]*D[y[x],x]==0; 
ic={y[0]==Exp[\[Alpha]],Derivative[1][y][1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{\alpha } \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
Alpha = symbols("Alpha") 
y = Function("y") 
ode = Eq(Alpha*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): exp(alpha), Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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