81.6.2 problem 7-2

Internal problem ID [21548]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-2
Date solved : Thursday, October 02, 2025 at 07:47:45 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\textit {x\_0} \right )&=y_{0} \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 17

ode:=diff(y(x),x)+q(x)*y(x) = 0; 
ic:=[y(x_0) = y__0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = y_{0} {\mathrm e}^{-\int _{\textit {x\_0}}^{x}q \left (\textit {\_z1} \right )d \textit {\_z1}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 36

ode=D[y[x],x]+q[x]*y[x]==0; 
ic={y[x0]==y0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {y0} \exp \left (\int _1^x-q(K[1])dK[1]-\int _1^{\text {x0}}-q(K[1])dK[1]\right ) \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
x0 = symbols("x0") 
y0 = symbols("y0") 
y = Function("y") 
q = Function("q") 
ode = Eq(q(x)*y(x) + Derivative(y(x), x),0) 
ics = {y(x0): y0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = y_{0} \left (e^{- \int q{\left (x \right )}\, dx}\right ) e^{\int q{\left (x_{0} \right )}\, dx_{0}} \]