7.4.21 problem 21

Internal problem ID [93]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 21
Date solved : Friday, February 07, 2025 at 07:49:06 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (2 \pi \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve([x*diff(y(x),x)=3*y(x)+x^4*cos(x),y(2*Pi) = 0],y(x), singsol=all)
 

\[ y = x^{3} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 11

DSolve[{x*D[y[x],x]==3*y[x]+x^4*Cos[x],{y[2*Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 \sin (x) \]