Internal problem ID [4133]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 897.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
\[ \boxed {x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }-2 y a=-a^{2}-x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 86
dsolve(x^2*diff(y(x),x)^2+2*a*x*diff(y(x),x)+a^2+x^2-2*a*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right )-\operatorname {RootOf}\left (-a \,\operatorname {arcsinh}\left (\frac {\operatorname {RootOf}\left (-2 a y \left (x \right )+a^{2}+x^{2}+2 a \textit {\_Z} +\textit {\_Z}^{2}\right )}{x}\right )-x \sqrt {-\frac {2 a \operatorname {RootOf}\left (-2 a y \left (x \right )+a^{2}+x^{2}+2 a \textit {\_Z} +\textit {\_Z}^{2}\right )}{x^{2}}-\frac {a^{2}}{x^{2}}+\frac {2 a \textit {\_Z}}{x^{2}}}+c_{1} \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.943 (sec). Leaf size: 82
DSolve[x^2 (y'[x])^2+2 a x y'[x]+a^2+x^2-2 a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=\frac {2 a x K[1]+x^2 K[1]^2+a^2+x^2}{2 a},x=\frac {a \log \left (\sqrt {K[1]^2+1}-K[1]\right )}{\sqrt {K[1]^2+1}}+\frac {c_1}{\sqrt {K[1]^2+1}}\right \},\{y(x),K[1]\}\right ] \]