29.27.22 problem 788

Internal problem ID [5372]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 788
Date solved : Sunday, March 30, 2025 at 08:03:49 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 20

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

\begin{align*} y &= -\frac {\left (a +x \right )^{2}}{4} \\ y &= c_1 \left (c_1 +a +x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 (a+x+c_1) \\ y(x)\to -\frac {1}{4} (a+x)^2 \\ \end{align*}

✓ Sympy. Time used: 2.265 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1}^{2} - C_{1} x - \frac {a^{2}}{4} - \frac {a x}{2} \]