85.34.10 problem 10

Internal problem ID [22718]
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 67
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:11:51 PM
CAS classification : [_dAlembert]

\begin{align*} {y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.113 (sec). Leaf size: 1001

ode:=diff(y(x),x)^2+(3*y(x)-2*x)*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 1.203 (sec). Leaf size: 259

ode=D[y[x],x]^2+(3*y[x]-2*x)*D[y[x],x]-6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\left (-\frac {\sqrt {2} \arctan \left (\frac {\sqrt {2} 3^{3/4} \sqrt [4]{8-3 K[1]} \sqrt [4]{K[1]}}{\sqrt {24-9 K[1]}-3 \sqrt {K[1]}}\right )}{\sqrt [4]{3}}-\frac {\sqrt {2} \text {arctanh}\left (\frac {\sqrt {2} \sqrt [4]{24-9 K[1]} \sqrt [4]{K[1]}}{\sqrt {8-3 K[1]}+\sqrt {3} \sqrt {K[1]}}\right )}{\sqrt [4]{3}}-\frac {(8-3 K[1])^{3/4} \sqrt [4]{K[1]}}{K[1]-2}\right ) \exp \left (-4 \left (\frac {3}{16} \log (8-3 K[1])-\frac {1}{4} \log (2-K[1])+\frac {1}{16} \log (K[1])\right )\right )+c_1 \exp \left (-4 \left (\frac {3}{16} \log (8-3 K[1])-\frac {1}{4} \log (2-K[1])+\frac {1}{16} \log (K[1])\right )\right ),y(x)=\frac {2 x K[1]}{3 (K[1]-2)}-\frac {K[1]^2}{3 (K[1]-2)}\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x + 3*y(x))*Derivative(y(x), x) - 6*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out