75.22.7 problem 712

Internal problem ID [17186]
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 : Tuesday, January 28, 2025 at 09:56:33 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*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 0, D(y)(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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