Internal problem ID [3383]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 644.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 34
dsolve((x*(a-x^2-y(x)^2)+y(x))*diff(y(x),x)+x-(a-x^2-y(x)^2)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (2 a \textit {\_Z} +\ln \left (-\frac {x^{2}}{a \left (\cos ^{2}\left (\textit {\_Z} \right )\right )-x^{2}}\right )+c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 47
DSolve[(x(a-x^2-y[x]^2)+y[x])y'[x]+x-(a-x^2-y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {-2 a \text {ArcTan}\left (\frac {y(x)}{x}\right )+\log \left (-a+x^2+y(x)^2\right )-\log \left (x^2+y(x)^2\right )}{2 a}=c_1,y(x)\right ] \]