83.49.8 problem Ex 8 page 126

Internal problem ID [19621]
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 8 page 126
Date solved : Tuesday, January 28, 2025 at 02:04:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 17

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

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