29.28.2 problem 799

Internal problem ID [5383]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 799
Date solved : Monday, January 27, 2025 at 11:17:35 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 29

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

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