40.6.5 problem 14

Internal problem ID [6685]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page 74
Problem number : 14
Date solved : Sunday, March 30, 2025 at 11:18:15 AM
CAS classification : [_quadrature]

\begin{align*} \left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 511

ode:=(3*y(x)-1)^2*diff(y(x),x)^2 = 4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {{\left (\left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{36 \left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ y &= \frac {{\left (i \sqrt {3}\, \left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}+\left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{144 \left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ y &= \frac {{\left (\left (i \sqrt {3}-1\right ) \left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}-12\right )}^{2}}{144 \left (108 c_1 -108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ y &= \frac {{\left (\left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{36 \left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ y &= \frac {{\left (i \left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}} \sqrt {3}+\left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}+12\right )}^{2}}{144 \left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ y &= \frac {{\left (\left (i \sqrt {3}-1\right ) \left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}-12\right )}^{2}}{144 \left (-108 c_1 +108 x +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 4.431 (sec). Leaf size: 892

ode=(3*y[x]-1)^2*D[y[x],x]^2==4*y[x]; 
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") 
y = Function("y") 
ode = Eq((3*y(x) - 1)**2*Derivative(y(x), x)**2 - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out