8.4.21 problem 21

Internal problem ID [724]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:59:15 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 11

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

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