8.4.18 problem 18

Internal problem ID [721]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:59:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 14

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

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