15.19.20 problem 20

Internal problem ID [3304]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 20
Date solved : Sunday, March 30, 2025 at 01:34:13 AM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

\begin{align*} 8 x +1&={y^{\prime }}^{2} y \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 137

ode:=8*x+1 = y(x)*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} -\frac {8 c_1 \left (8 x +1\right )}{y \left (\frac {8 x +1-2 \sqrt {y \left (8 x +1\right )}+4 y}{y}\right )^{{2}/{3}} \left (\frac {-\sqrt {y \left (8 x +1\right )}-2 y}{y}\right )^{{2}/{3}}}+x +\frac {1}{8} &= 0 \\ \frac {1}{8}-\frac {8 c_1 \left (8 x +1\right )}{y \left (\frac {8 x +1+2 \sqrt {y \left (8 x +1\right )}+4 y}{y}\right )^{{2}/{3}} \left (\frac {\sqrt {y \left (8 x +1\right )}-2 y}{y}\right )^{{2}/{3}}}+x &= 0 \\ \end{align*}

✓ Mathematica. Time used: 3.706 (sec). Leaf size: 79

ode=8*x+1==D[y[x],x]^2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (-8 \sqrt {8 x+1} x-\sqrt {8 x+1}+12 c_1\right ){}^{2/3} \\ y(x)\to \frac {1}{4} \left (8 \sqrt {8 x+1} x+\sqrt {8 x+1}+12 c_1\right ){}^{2/3} \\ \end{align*}

✓ Sympy. Time used: 108.721 (sec). Leaf size: 1108

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x - y(x)*Derivative(y(x), x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]