29.30.6 problem 864

Internal problem ID [5446]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 864
Date solved : Tuesday, March 04, 2025 at 09:39:41 PM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}+a +b x -y-b y&=0 \end{align*}

✓ Maple. Time used: 0.089 (sec). Leaf size: 116

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

\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z} \sqrt {\frac {x}{c_{1}}}-b \sqrt {\frac {x}{c_{1}}}-\textit {\_Z}^{\frac {1}{b}} \left (\frac {x}{c_{1}}\right )^{\frac {1}{2 b}}+\sqrt {\frac {x}{c_{1}}}\right )^{2} x +2 \operatorname {RootOf}\left (\textit {\_Z} \sqrt {\frac {x}{c_{1}}}-b \sqrt {\frac {x}{c_{1}}}-\textit {\_Z}^{\frac {1}{b}} \left (\frac {x}{c_{1}}\right )^{\frac {1}{2 b}}+\sqrt {\frac {x}{c_{1}}}\right ) x +\left (b +1\right ) x +a}{b +1} \]

✓ Mathematica. Time used: 147.912 (sec). Leaf size: 1133

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

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

✗ Sympy

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

Timed Out