Internal problem ID [10212]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
28. Summary. Page 59
Problem number: Ex 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
Solve \begin {gather*} \boxed {y^{\prime } y-\left (x -b \right ) \left (y^{\prime }\right )^{2}-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
dsolve(y(x)*diff(y(x),x)=(x-b)*diff(y(x),x)^2+a,y(x), singsol=all)
\begin{align*} y \relax (x ) = x c_{1}+\frac {-b c_{1}^{2}+a}{c_{1}} \\ y \relax (x ) = c_{1} \sqrt {b -x} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y(x)*y'[x]==(x-b)*(y'[x])^2+a,y[x],x,IncludeSingularSolutions -> True]
Not solved