29.21.30 problem 606

Internal problem ID [5200]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 606
Date solved : Monday, January 27, 2025 at 10:20:39 AM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 36

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

\[ \frac {{\mathrm e}^{-2 i y \left (x \right )} \left (i x +y \left (x \right )\right )+2 c_{1} \left (i y \left (x \right )+x \right )}{2 i y \left (x \right )+2 x} = 0 \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 18

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

\[ \text {Solve}\left [y(x)-\arctan \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]