12.5.22 problem 19

Internal problem ID [1646]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:15:54 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: 0.007 (sec). Leaf size: 11

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

\[ y = \tan \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 13

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

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