29.30.19 problem 878

Internal problem ID [5459]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 878
Date solved : Monday, January 27, 2025 at 11:24:40 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 59

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

\begin{align*} y(x)\to c_1 (x-a)+\frac {b}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {b (x-a)} \\ y(x)\to 2 \sqrt {b (x-a)} \\ \end{align*}