85.35.1 problem 1

Internal problem ID [22721]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 68
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:13:10 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 41

ode:=diff(y(x),x) = ((5*x-6*y(x))/(5*x+6*y(x)))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}-\frac {1}{-\sqrt {-\frac {6 \textit {\_a} -5}{6 \textit {\_a} +5}}+\textit {\_a}}d \textit {\_a} +\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.363 (sec). Leaf size: 231

ode=D[y[x],x]==Sqrt[ (5*x-6*y[x])/(5*x+6*y[x]) ] ; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{341} \left (-341 \log \left (\sqrt {\frac {6 y(x)}{x}-5}-\sqrt {\frac {6 y(x)}{x}+5}\right )+176 \log \left (2 \sqrt {\frac {6 y(x)}{x}-5}+i \sqrt {\frac {6 y(x)}{x}+5}\right )-341 \log \left (\sqrt {\frac {6 y(x)}{x}-5}+\sqrt {\frac {6 y(x)}{x}+5}\right )+\left (253+34 i \sqrt {11}\right ) \log \left (3 \sqrt {\frac {6 y(x)}{x}-5}+\sqrt {7-4 i \sqrt {11}} \sqrt {\frac {6 y(x)}{x}+5}\right )+\left (253-34 i \sqrt {11}\right ) \log \left (3 \sqrt {\frac {6 y(x)}{x}-5}-\sqrt {7+4 i \sqrt {11}} \sqrt {\frac {6 y(x)}{x}+5}\right )\right )=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 4.207 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt((5*x - 6*y(x))/(5*x + 6*y(x))) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \int \limits ^{\frac {x}{y{\left (x \right )}}} \frac {\sqrt {\frac {5 u_{1} - 6}{5 u_{1} + 6}}}{u_{1} \sqrt {\frac {5 u_{1} - 6}{5 u_{1} + 6}} - 1}\, du_{1}} \]