73.5.28 problem 6.7 (p)

Internal problem ID [15139]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:31 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (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: 0.225 (sec). Leaf size: 15

DSolve[D[y[x],x]==x*(1+2*y[x]/x^2+y[x]^2/x^4),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \tan (\log (x)+c_1) \]