28.1.40 problem 41

Internal problem ID [4346]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 41
Date solved : Monday, January 27, 2025 at 09:06:22 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x^{2}+y+y^{2}-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve((x^2+y(x)+y(x)^2)-x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.201 (sec). Leaf size: 12

DSolve[(x^2+y[x]+y[x]^2)-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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