67.4.25 problem 5.3 (e)

Internal problem ID [16394]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (e)
Date solved : Thursday, October 02, 2025 at 01:27:35 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=y+x^{2} \cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 10

ode:=x*diff(y(x),x) = y(x)+x^2*cos(x); 
ic:=[y(1/2*Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (\sin \left (x \right )-1\right ) x \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 21

ode=x*D[y[x],x]==y[x]+x^2*Cos[x]; 
ic={y[Pi/2]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \int _{\frac {\pi }{2}}^x\cos (K[1])dK[1] \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 8

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

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