83.41.3 problem 2 (ii)

Internal problem ID [19483]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 2 (ii)
Date solved : Tuesday, January 28, 2025 at 01:46:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 28

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

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