15.21.1 problem 23

Internal problem ID [3325]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:34:13 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 23

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

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