65.5.8 problem 10.4 (i)

Internal problem ID [13747]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.4 (i)
Date solved : Tuesday, January 28, 2025 at 06:01:08 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=\log (x)+c_1,y(x)\right ] \]