60.1.375 problem 384

Internal problem ID [10389]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 384
Date solved : Sunday, March 30, 2025 at 04:34:27 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 50

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 51

ode=c - a*y[x] + (b + 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 \frac {c+c_1 (a x+b+c_1)}{a} \\ y(x)\to -\frac {a^2 x^2+2 a b x+b^2-4 c}{4 a} \\ \end{align*}

✓ Sympy. Time used: 2.892 (sec). Leaf size: 31

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

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