85.13.5 problem 5

Internal problem ID [22511]
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. B Exercises at page 40
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:44:09 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {2 x +3 y} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 47

ode:=diff(y(x),x) = (2*x+3*y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {2 \ln \left (-4+27 y+18 x \right )}{9}-\frac {2 \sqrt {2 x +3 y}}{3}+\frac {4 \,\operatorname {arctanh}\left (\frac {3 \sqrt {2 x +3 y}}{2}\right )}{9}-c_1 = 0 \]

✓ Mathematica. Time used: 7.342 (sec). Leaf size: 73

ode=D[y[x],x]==Sqrt[2*x+3*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2}{27} \left (-2 W\left (-\frac {1}{2} e^{-\frac {9 x}{4}-1+\frac {9 c_1}{4}}\right ){}^2-4 W\left (-\frac {1}{2} e^{-\frac {9 x}{4}-1+\frac {9 c_1}{4}}\right )+9 x-2\right )\\ y(x)&\to \frac {4}{27}-\frac {2 x}{3} \end{align*}

✓ Sympy. Time used: 1.583 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(2*x + 3*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x - \frac {2 \sqrt {3} \sqrt {\frac {2 x}{3} + y{\left (x \right )}}}{3} + \frac {4 \log {\left (3 \sqrt {3} \sqrt {\frac {2 x}{3} + y{\left (x \right )}} + 2 \right )}}{9} = 0 \]