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
:
Wednesday, March 05, 2025 at 02:35:24 AM
CAS
classification
:
[_quadrature]
\begin{align*} \left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \end{align*}
✓ Maple. Time used: 0.023 (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 x +108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{36 \left (-108 x +108 c_1 +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 x +108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}+\left (-108 x +108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{144 \left (-108 x +108 c_1 +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 x +108 c_1 +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 x +108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}} \\
y &= \frac {{\left (\left (108 x -108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{36 \left (108 x -108 c_1 +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 x -108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}-12 i \sqrt {3}+\left (108 x -108 c_1 +12 \sqrt {81 c_1^{2}-162 c_1 x +81 x^{2}-12}\right )^{{2}/{3}}+12\right )}^{2}}{144 \left (108 x -108 c_1 +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 x -108 c_1 +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 x -108 c_1 +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