44.6.9 problem 9

Internal problem ID [7153]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 9
Date solved : Tuesday, February 04, 2025 at 12:40:25 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y = x \left (-\cos \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 14

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

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