77.5.12 problem 12

Internal problem ID [20392]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 12
Date solved : Thursday, October 02, 2025 at 05:50:44 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=diff(y(x),x)+2*y(x)/x = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\cos \left (x \right ) x^{2}+2 \cos \left (x \right )+2 \sin \left (x \right ) x +c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {-\left (x^2-2\right ) \cos (x)+2 x \sin (x)+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.212 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} - \cos {\left (x \right )} + \frac {2 \sin {\left (x \right )}}{x} + \frac {2 \cos {\left (x \right )}}{x^{2}} \]