23.2.133 problem 136

Internal problem ID [5488]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 136
Date solved : Tuesday, September 30, 2025 at 12:45:20 PM
CAS classification : [_rational, _dAlembert]

\begin{align*} \left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.091 (sec). Leaf size: 249

ode:=(5+3*x)*diff(y(x),x)^2-(3+3*y(x))*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \frac {-108 \left (c_1 -\frac {\operatorname {Ei}_{1}\left (\frac {-9-9 y-3 \sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{6 x +10}\right )}{2}\right ) \left (x -\frac {3 y}{2}-\frac {\sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{2}+\frac {1}{6}\right ) {\mathrm e}^{\frac {-9-9 y-3 \sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{6 x +10}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\ \frac {108 \left (c_1 +\frac {\operatorname {Ei}_{1}\left (\frac {-9-9 y+3 \sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{6 x +10}\right )}{2}\right ) \left (x -\frac {3 y}{2}+\frac {\sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{2}+\frac {1}{6}\right ) {\mathrm e}^{\frac {-9-9 y+3 \sqrt {9+9 y^{2}+\left (-12 x -2\right ) y}}{6 x +10}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.626 (sec). Leaf size: 286

ode=(5+3 x) (D[y[x],x])^2-(3+3 y[x])D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\exp \left (\int _1^{K[1]}\frac {\frac {6 K[2]}{3 K[2]-1}-\frac {9 K[2]^2}{(3 K[2]-1)^2}}{K[2]-\frac {3 K[2]^2}{3 K[2]-1}}dK[2]\right ) \int \frac {\left (\frac {10 K[1]-3}{3 K[1]-1}-\frac {3 \left (5 K[1]^2-3 K[1]\right )}{(3 K[1]-1)^2}\right ) \exp \left (-\int _1^{K[1]}\frac {\frac {6 K[2]}{3 K[2]-1}-\frac {9 K[2]^2}{(3 K[2]-1)^2}}{K[2]-\frac {3 K[2]^2}{3 K[2]-1}}dK[2]\right )}{K[1]-\frac {3 K[1]^2}{3 K[1]-1}} \, dK[1]+c_1 \exp \left (\int _1^{K[1]}\frac {\frac {6 K[2]}{3 K[2]-1}-\frac {9 K[2]^2}{(3 K[2]-1)^2}}{K[2]-\frac {3 K[2]^2}{3 K[2]-1}}dK[2]\right ),y(x)=\frac {3 x K[1]^2}{3 K[1]-1}+\frac {5 K[1]^2-3 K[1]}{3 K[1]-1}\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x + 5)*Derivative(y(x), x)**2 - (3*y(x) + 3)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out