Internal problem ID [3348]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 606.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (x +x^{2}+y^{2}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 30
dsolve((x+x^2+y(x)^2)*diff(y(x),x) = y(x),y(x), singsol=all)
\[ c_{1}+\frac {{\mathrm e}^{-2 i y \relax (x )} \left (i x +y \relax (x )\right )}{2 i y \relax (x )+2 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 18
DSolve[(x+x^2+y[x]^2)y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-\text {ArcTan}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]