19.2.2 problem 2

Internal problem ID [3531]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:40:49 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)-4*x*y(x)=x^7*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\sin \left (x \right )-\cos \left (x \right ) x +c_{1} \right ) x^{4} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 19

DSolve[x^2*D[y[x],x]-4*x*y[x]==x^7*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^4 (\sin (x)-x \cos (x)+c_1) \]