83.26.2 problem 2

Internal problem ID [19326]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:34:12 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x^{5} \end{align*}

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+5*y(x)=x^5,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2}}{x^{5}}+\frac {x^{5}}{60}+\frac {c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+5*y[x]==x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^5}{60}+\frac {c_1}{x^5}+\frac {c_2}{x} \]