20.1.24 problem Problem 32

Internal problem ID [3581]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 32
Date solved : Sunday, March 30, 2025 at 01:52:37 AM
CAS classification : [_Bernoulli]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=\frac {1}{\pi } \end{align*}

✓ Maple. Time used: 0.209 (sec). Leaf size: 14

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

\[ y = \frac {\sqrt {\sin \left (x \right )+1}}{x} \]

✓ Mathematica. Time used: 0.287 (sec). Leaf size: 17

ode=D[y[x],x]==(Cos[x]-2*x*y[x]^2)/(2*x^2*y[x]); 
ic={y[Pi]==1/Pi}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sqrt {\sin (x)+1}}{x} \]

✓ Sympy. Time used: 0.580 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {\sqrt {\sin {\left (x \right )} + 1}}{x} \]