Internal problem ID [13083]
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 (p).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]
\[ \boxed {y^{\prime }-x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x*(1+2*y(x)/x^2+y(x)^2/x^4),y(x), singsol=all)
\[ y = -\tan \left (-\ln \left (x \right )+c_{1} \right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 15
DSolve[y'[x]==x*(1+2*y[x]/x^2+y[x]^2/x^4),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \tan (\log (x)+c_1) \]