30.6.23 problem 24

Internal problem ID [7558]
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 : 24
Date solved : Tuesday, September 30, 2025 at 04:49:12 PM
CAS classification : [NONE]

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

✗ Maple

ode:=(y(x)/x)^(1/2)+cos(x)+((x/y(x))^(1/2)+sin(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 2.074 (sec). Leaf size: 55

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

\[ \text {Solve}\left [2 x \sqrt {\frac {y(x)}{x}}+2 \sqrt {\frac {x}{y(x)}} y(x)-\frac {2 y(x)}{\sqrt {\frac {y(x)}{x}}}-\cos (y(x))+\sin (x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out