Internal problem ID [3891]
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]
\[ \boxed {\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }-\left (a -x^{2}-y^{2}\right ) y=-x} \]
✓ Solution by Maple
Time used: 0.5 (sec). Leaf size: 37
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)
\[ y \left (x \right ) = \cot \left (\operatorname {RootOf}\left (2 c_{1} a -2 a \textit {\_Z} +\ln \left (-\frac {x^{2}}{a \sin \left (\textit {\_Z} \right )^{2}-x^{2}}\right )\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.181 (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]
\[ \text {Solve}\left [\frac {\log \left (-a+x^2+y(x)^2\right )-2 a \tan ^{-1}\left (\frac {y(x)}{x}\right )-\log \left (x^2+y(x)^2\right )}{2 a}=c_1,y(x)\right ] \]