Internal problem ID [2020]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y x -\frac {x}{y}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x)-x*y(x)=x/y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} -1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.967 (sec). Leaf size: 57
DSolve[y'[x]-x*y[x]==x/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to \sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}