Internal problem ID [11226]
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], _Clairaut]
\[ \boxed {y y^{\prime }-\left (x -b \right ) {y^{\prime }}^{2}=a} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 49
dsolve(y(x)*diff(y(x),x)=(x-b)*diff(y(x),x)^2+a,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \sqrt {-a \left (b -x \right )} \\ y \left (x \right ) &= 2 \sqrt {-a \left (b -x \right )} \\ y \left (x \right ) &= \frac {\left (-b +x \right ) c_{1}^{2}+a}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 59
DSolve[y[x]*y'[x]==(x-b)*(y'[x])^2+a,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a}{c_1}+c_1 (x-b) \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {a (x-b)} \\ y(x)\to 2 \sqrt {a (x-b)} \\ \end{align*}