29.30.37 problem 897

Internal problem ID [5477]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 897
Date solved : Monday, January 27, 2025 at 11:25:34 AM
CAS classification : [_rational]

\begin{align*} x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 78

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)
 

\[ y \left (x \right )-\operatorname {RootOf}\left (-x \sqrt {\frac {a \left (-2 \operatorname {RootOf}\left (-2 a y \left (x \right )+a^{2}+x^{2}+2 \textit {\_Z} a +\textit {\_Z}^{2}\right )+2 \textit {\_Z} -a \right )}{x^{2}}}-a \,\operatorname {arcsinh}\left (\frac {\operatorname {RootOf}\left (-2 a y \left (x \right )+a^{2}+x^{2}+2 \textit {\_Z} a +\textit {\_Z}^{2}\right )}{x}\right )+c_{1} \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.706 (sec). Leaf size: 70

DSolve[x^2 (D[y[x],x])^2+2 a x D[y[x],x]+a^2+x^2-2 a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{y(x)=\frac {2 a x K[1]+x^2 K[1]^2+a^2+x^2}{2 a},x=-\frac {a \text {arcsinh}(K[1])}{\sqrt {K[1]^2+1}}+\frac {c_1}{\sqrt {K[1]^2+1}}\right \},\{y(x),K[1]\}\right ] \]