8.11.34 problem 57

Internal problem ID [902]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 57
Date solved : Monday, January 27, 2025 at 03:17:43 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=72 x^{5} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=72*x^5,y(x), singsol=all)
 

\[ y = \frac {3 x^{6}+c_2 \,x^{2}+c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==72*x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^5+c_2 x+\frac {c_1}{x} \]