15.5.13 problem 13

Internal problem ID [2949]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:00:16 AM
CAS classification : [_rational]

\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \end{align*}

Solution by Maple

Time used: 0.045 (sec). Leaf size: 36

dsolve((x^2+y(x)^2+x)*diff(y(x),x)=y(x),y(x), singsol=all)
 
\[ \frac {{\mathrm e}^{-2 i y} \left (i x +y\right )+2 \left (i y+x \right ) c_1}{2 i y+2 x} = 0 \]

Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 18

DSolve[(x^2+y[x]^2+x)*D[y[x],x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 
\[ \text {Solve}\left [y(x)-\arctan \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]