66.1.37 problem Problem 51

Internal problem ID [13884]
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 51
Date solved : Tuesday, January 28, 2025 at 06:07:13 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 79

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

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out