29.29.10 problem 832

Internal problem ID [5415]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 832
Date solved : Monday, January 27, 2025 at 11:21:33 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 22

dsolve(2*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}}{8} \\ y \left (x \right ) &= c_{1} \left (2 c_{1} +x -1\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 28

DSolve[2 (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+2 c_1) \\ y(x)\to -\frac {1}{8} (x-1)^2 \\ \end{align*}