77.1.61 problem 80 (page 120)

Internal problem ID [17951]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 80 (page 120)
Date solved : Tuesday, January 28, 2025 at 11:16:25 AM
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: 0.086 (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 &= \frac {\left (x +1\right )^{2}}{4} \\ y &= c_{1} \left (x +1-c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (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*}