69.1.2 problem 2

Internal problem ID [14155]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:16:17 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 28

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

\begin{align*} y(x)\to c_1 (x+1-c_1) \\ y(x)\to \frac {1}{4} (x+1)^2 \\ \end{align*}