23.1.11 problem 2(a)

Internal problem ID [4101]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(a)
Date solved : Tuesday, March 04, 2025 at 05:26:00 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 14

ode:=diff(y(x),x)-y(x)*tan(x) = x; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y \left (x \right ) = 1+\tan \left (x \right ) x -\sec \left (x \right ) \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 15

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

\[ y(x)\to x \tan (x)-\sec (x)+1 \]

✓ Sympy. Time used: 0.604 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = x \tan {\left (x \right )} + 1 - \frac {1}{\cos {\left (x \right )}} \]