80.6.10 problem 9 (d)

Internal problem ID [18495]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 9 (d)
Date solved : Thursday, March 13, 2025 at 12:07:57 PM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 21

ode:=diff(y(x),x)/x = y(x)*sin(x^2-1)-2*y(x)/x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {\cos \left (x^{2}-1\right )}{2}-\frac {4 x^{{3}/{2}}}{3}} \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 37

ode=1/x*D[y[x],x]==y[x]*Sin[x^2-1]-2*y[x]/Sqrt[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 e^{\frac {1}{6} \left (-8 x^{3/2}-3 \cos \left (1-x^2\right )\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.623 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*sin(x**2 - 1) + Derivative(y(x), x)/x + 2*y(x)/sqrt(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {4 x^{\frac {3}{2}}}{3} - \frac {\cos {\left (x^{2} - 1 \right )}}{2}} \]