71.4.19 problem 19

Internal problem ID [14312]
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 : 19
Date solved : Wednesday, March 05, 2025 at 10:45:18 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.464 (sec). Leaf size: 18

ode:=diff(y(x),x) = y(x)/x+tan(x); 
ic:=y(Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \left (\int _{\pi }^{x}\frac {\tan \left (\textit {\_z1} \right )}{\textit {\_z1}}d \textit {\_z1} \right ) x \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 22

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

\[ y(x)\to x \int _{\pi }^x\frac {\tan (K[1])}{K[1]}dK[1] \]

✓ Sympy. Time used: 0.963 (sec). Leaf size: 32

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

\[ - \int \frac {y{\left (x \right )}}{x^{2}}\, dx - \int \frac {\tan {\left (x \right )}}{x}\, dx = - \int \limits ^{\pi } \frac {y{\left (x \right )}}{x^{2}}\, dx - \int \limits ^{\pi } \frac {\tan {\left (x \right )}}{x}\, dx \]