36.3.1 problem 1

Internal problem ID [6322]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 1
Date solved : Monday, January 27, 2025 at 01:56:30 PM
CAS classification : [_linear]

\begin{align*} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

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

\[ y \left (x \right ) = \left (\sin \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 12

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

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