Internal problem ID [4115]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 878.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {\left (-x +a \right ) {y^{\prime }}^{2}+y y^{\prime }=b} \]
✓ Solution by Maple
Time used: 0.141 (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 (a -x \right )} \\ y \left (x \right ) &= 2 \sqrt {-b \left (a -x \right )} \\ y \left (x \right ) &= \frac {\left (x -a \right ) c_{1}^{2}+b}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 59
DSolve[(a-x) (y'[x])^2+y[x] y'[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*}