Internal problem ID [4978]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y x^{2}-y^{\prime } x^{3}=-x^{4} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.037 (sec). Leaf size: 12
DSolve[(x^2*y[x]+x^4*Cos[x])-x^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\sin (x)+c_1) \]