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 : Sunday, March 30, 2025 at 10:51:31 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \left (\sin \left (x \right )+c_1 \right ) x \]

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

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

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

✓ Sympy. Time used: 0.335 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*cos(x) - x**3*Derivative(y(x), x) + x**2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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