30.6.33 problem 34

Internal problem ID [7568]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 34
Date solved : Tuesday, September 30, 2025 at 04:53:13 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 16

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

\[ y = \left (\sin \left (x \right )+\frac {2}{\pi ^{2}}\right ) x^{2} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to x^2 \left (\sin (x)+\frac {2}{\pi ^2}\right ) \end{align*}

✓ Sympy. Time used: 0.227 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = x^{2} \left (\sin {\left (x \right )} + \frac {2}{\pi ^{2}}\right ) \]