75.22.8 problem 713

Internal problem ID [17108]
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 : 713
Date solved : Thursday, March 13, 2025 at 09:16:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+2*y(x) = 0; 
ic:=y(0) = 0, D(y)(Pi) = exp(Pi); 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -{\mathrm e}^{x} \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 12

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

\[ y(x)\to -e^x \sin (x) \]

✓ Sympy. Time used: 0.165 (sec). Leaf size: 10

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

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