66.1.33 problem Problem 47

Internal problem ID [13880]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 47
Date solved : Tuesday, January 28, 2025 at 06:07:07 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

With initial conditions

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

✓ Solution by Maple

Time used: 15.013 (sec). Leaf size: 17

dsolve([y(x)=x*diff(y(x),x)+diff(y(x),x)^2,y(2) = -1],y(x), singsol=all)
 

\begin{align*} y &= 1-x \\ y &= -\frac {x^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 21

DSolve[{y[x]==x*D[y[x],x]+D[y[x],x]^2,{y[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1-x \\ y(x)\to -\frac {x^2}{4} \\ \end{align*}