60.1.369 problem 378

Internal problem ID [10383]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 378
Date solved : Sunday, March 30, 2025 at 04:34:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.032 (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 (x +a \right )^{2}}{4} \\ y &= c_1 \left (c_1 +a +x \right ) \\ \end{align*}

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

ode=-y[x] + (a + x)*D[y[x],x] + D[y[x],x]^2==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: 2.335 (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)
 

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