31.6.12 problem 12

Internal problem ID [5761]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 12
Date solved : Monday, January 27, 2025 at 01:12:59 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

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

DSolve[y[x]==x*D[y[x],x]+D[y[x],x]-(D[y[x],x])^2,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*}