29.27.19 problem 785

Internal problem ID [5369]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 785
Date solved : Monday, January 27, 2025 at 11:17:25 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 22

dsolve(diff(y(x),x)^2+(1-x)*diff(y(x),x)+y(x) = 0,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: 0.011 (sec). Leaf size: 28

DSolve[(D[y[x],x])^2+(1-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*}