29.27.28 problem 794

Internal problem ID [5378]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 794
Date solved : Sunday, March 30, 2025 at 08:03:58 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 50

ode:=diff(y(x),x)^2-(2*x+1)*diff(y(x),x)-x*(1-x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (-8 x -1\right ) \sqrt {8 x +1}}{24}+\frac {x^{2}}{2}+\frac {x}{2}+c_1 \\ y &= \frac {x}{2}+\frac {\left (8 x +1\right )^{{3}/{2}}}{24}+\frac {x^{2}}{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 62

ode=(D[y[x],x])^2-(1+2*x)*D[y[x],x]-x*(1-x)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {x^2}{2}+\frac {x}{2}-\frac {1}{24} (8 x+1)^{3/2}+c_1 \\ y(x)\to \frac {1}{2} \left (x^2+x+\frac {1}{12} (8 x+1)^{3/2}\right )+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 44

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {x^{2}}{2} + \frac {x}{2} - \frac {\left (8 x + 1\right )^{\frac {3}{2}}}{24}, \ y{\left (x \right )} = C_{1} + \frac {x^{2}}{2} + \frac {x}{2} + \frac {\left (8 x + 1\right )^{\frac {3}{2}}}{24}\right ] \]