83.41.27 problem 9

Internal problem ID [19507]
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 : 9
Date solved : Tuesday, January 28, 2025 at 01:47:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 16

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

\[ y(x)\to x \left (c_2 e^x+c_1\right ) \]