Internal problem ID [10216]
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 6.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (y^{\prime } x -y\right ) \left (x +y^{\prime } y\right )-a^{2} y^{\prime }=0} \end {gather*}
✗ Solution by Maple
dsolve((diff(y(x),x)*x-y(x))*(diff(y(x),x)*y(x)+x)=a^2*diff(y(x),x),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 75
DSolve[(y'[x]*x-y[x])*(y'[x]*y[x]+x)==a^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {c_1 \left (x^2-\frac {a^2}{1+c_1}\right )} \\ y(x)\to -i (a-x) \\ y(x)\to i (a-x) \\ y(x)\to -i (a+x) \\ y(x)\to i (a+x) \\ \end{align*}