Internal problem ID [252]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y=72 x^{5}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {3 x^{6}+c_{2} x^{2}+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 21
DSolve[x^2*y''[x]+x*y'[x]-y[x]==72*x^5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^5+c_2 x+\frac {c_1}{x} \]