44.3.19 problem 27

Internal problem ID [7000]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 27
Date solved : Monday, January 27, 2025 at 02:40:30 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

dsolve(diff(y(x),x)+y(x)*sin(x)=x,y(x), singsol=all)
 

\[ y = \left (\int x \,{\mathrm e}^{-\cos \left (x \right )}d x +c_{1} \right ) {\mathrm e}^{\cos \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.679 (sec). Leaf size: 30

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

\[ y(x)\to e^{\cos (x)} \left (\int _1^xe^{-\cos (K[1])} K[1]dK[1]+c_1\right ) \]