Internal problem ID [13398]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime } x -y-\sqrt {y x +x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x*diff(y(x),x)-y(x)=sqrt(x*y(x)+x^2),y(x), singsol=all)
\[ -\frac {x +y \left (x \right )}{\sqrt {x \left (x +y \left (x \right )\right )}}+\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.194 (sec). Leaf size: 26
DSolve[x*y'[x]-y[x]==Sqrt[x*y[x]+x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x \left (\log ^2(x)+2 c_1 \log (x)-4+c_1{}^2\right ) \]