29.30.27 problem 887

Internal problem ID [5467]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 887
Date solved : Tuesday, March 04, 2025 at 09:40:28 PM
CAS classification : [[_homogeneous, `class G`], _rational, _dAlembert]

\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 149

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

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

✓ Mathematica. Time used: 60.236 (sec). Leaf size: 4057

ode=4 x (D[y[x],x])^2+4 y[x] D[y[x],x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x)**2 + 4*y(x)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out