20.4.1 problem Problem 9

Internal problem ID [3636]
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 9
Date solved : Monday, January 27, 2025 at 07:48:05 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

dsolve(diff(y(x),x)=(y(x)^2+x*y(x)+x^2)/x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \tan \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 13

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

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