83.5.4 problem 4

Internal problem ID [19020]
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 : 4
Date solved : Thursday, March 13, 2025 at 01:23:27 PM
CAS classification : [_linear]

\begin{align*} y-x \sin \left (x^{2}\right )+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=y(x)-x*sin(x^2)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 21

ode=(y[x]-x*Sin[x^2])+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.318 (sec). Leaf size: 12

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

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