83.37.13 problem 13

Internal problem ID [19458]
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 VIII (B) at page 128
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:45:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 42

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

\[ y(x)\to c_1 e^{-i a x} x^n-\frac {i c_2 e^{i a x} x^n}{2 a} \]