78.8.43 problem 43

Internal problem ID [18241]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 43
Date solved : Tuesday, January 28, 2025 at 11:43:26 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 13

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

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