7.4.18 problem 18

Internal problem ID [90]
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 : 18
Date solved : Friday, February 07, 2025 at 07:49:00 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve(x*diff(y(x),x)=2*y(x)+x^3*cos(x),y(x), singsol=all)
 

\[ y = x^{2} \left (\sin \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

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

DSolve[x*D[y[x],x]==2*y[x]+x^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (\sin (x)+c_1) \]