83.41.14 problem 5 (i)

Internal problem ID [19494]
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 : 5 (i)
Date solved : Tuesday, January 28, 2025 at 01:46:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve((x^3-2*x^2)*diff(y(x),x$2)+2*x^2*diff(y(x),x)-12*(x-2)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2} x^{7}+c_{1}}{x^{3} \left (x -2\right )} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 28

DSolve[(x^3-2*x^2)*D[y[x],{x,2}]+2*x^2*D[y[x],x]-12*(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^7+7 c_1}{7 (x-2) x^3} \]