Internal problem ID [2089]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-\sin \relax (x ) x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x^4*sin(x),y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+c_{1} x^{3}-x^{2} \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==x^4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (-\sin (x)+c_2 x+c_1) \\ \end{align*}