29.27.27 problem 793

Internal problem ID [5377]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 793
Date solved : Monday, January 27, 2025 at 11:17:31 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 29

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

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