83.30.13 problem 13

Internal problem ID [19392]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:37:11 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve((a^2-x^2)*diff(y(x),x$2)-a^2/x*diff(y(x),x)+x^2/a=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {2 c_{1} a \sqrt {-a +x}\, \sqrt {a +x}+2 c_{2} a +x^{2}}{2 a} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \sqrt {x^2-a^2}+\frac {x^2}{2}+c_2 \]