49.21.11 problem 4(c)

Internal problem ID [7741]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 4(c)
Date solved : Monday, January 27, 2025 at 03:11:27 PM
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: 0.005 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 13

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

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