83.49.9 problem Ex 9 page 126

Internal problem ID [19622]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 9 page 126
Date solved : Tuesday, January 28, 2025 at 02:04:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 33

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

\[ y(x)\to c_1 e^{-i x} x-\frac {1}{2} i c_2 e^{i x} x \]