75.22.7 problem 712

Internal problem ID [17107]
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 : 712
Date solved : Thursday, March 13, 2025 at 09:16:13 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^{\prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.131 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=y(0) = 0, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{1-x} \left ({\mathrm e}^{2 x}-1\right )}{{\mathrm e}^{2}+1} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 27

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

\[ y(x)\to \frac {e^{1-x} \left (e^{2 x}-1\right )}{1+e^2} \]

✓ Sympy. Time used: 0.078 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = \frac {e e^{x}}{1 + e^{2}} - \frac {e e^{- x}}{1 + e^{2}} \]