83.41.10 problem 2 (ix)

Internal problem ID [19490]
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 : 2 (ix)
Date solved : Tuesday, January 28, 2025 at 01:46:27 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=8 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=8*x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{4}+c_{2} x^{2}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==8*x^3,y[x],x,IncludeSingularSolutions -> True]
 

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