20.1.12 problem Problem 18

Internal problem ID [3569]
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
Date solved : Monday, January 27, 2025 at 07:44:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 20

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (-\sin (x)+c_2 x+c_1) \]