60.1.383 problem 384

Internal problem ID [10397]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 384
Date solved : Monday, January 27, 2025 at 07:39:02 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*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 50

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

\begin{align*} y &= \frac {-a^{2} x^{2}-2 a x b -b^{2}+4 c}{4 a} \\ y &= \frac {c_{1}^{2}+\left (a x +b \right ) c_{1} +c}{a} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[c - a*y[x] + (b + a*x)*D[y[x],x] + D[y[x],x]^2==0,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*}