Internal problem ID [2670]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x y^{\prime }-y-\sqrt {9 x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(x*diff(y(x),x)-y(x)=sqrt(9*x^2+y(x)^2),y(x), singsol=all)
\[ \frac {-c_{1} x^{2}+\sqrt {9 x^{2}+y \left (x \right )^{2}}+y \left (x \right )}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 27
DSolve[x*y'[x]-y[x]==Sqrt[9*x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {9 e^{c_1} x^2}{2}-\frac {e^{-c_1}}{2} \]