65.4.18 problem 18

Internal problem ID [15677]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:22:52 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 17

ode:=diff(y(x),x) = y(x)/x+cos(x); 
ic:=[y(-1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\left (i \pi +\operatorname {Ci}\left (1\right )-\operatorname {Ci}\left (x \right )\right ) x \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 14

ode=D[y[x],x]==y[x]/x+Cos[x]; 
ic={y[-1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (\operatorname {CosIntegral}(x)-\operatorname {CosIntegral}(-1)) \end{align*}

✓ Sympy. Time used: 0.387 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x \left (\operatorname {Ci}{\left (x \right )} - \operatorname {Ci}{\left (-1 \right )}\right ) \]