29.27.21 problem 787

Internal problem ID [5371]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 787
Date solved : Monday, January 27, 2025 at 11:17:26 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 24

dsolve(diff(y(x),x)^2-(2-x)*diff(y(x),x)+1-y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 29

DSolve[(D[y[x],x])^2-(2-x)*D[y[x],x]+1-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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