74.1.50 problem 57

Internal problem ID [15830]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 57
Date solved : Tuesday, January 28, 2025 at 08:08:27 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (\frac {2}{\pi }\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 12

dsolve([diff(y(x),x)=cos(1/x)/x^2,y(2/Pi) = 1],y(x), singsol=all)
 

\[ y = -\sin \left (\frac {1}{x}\right )+2 \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 13

DSolve[{D[y[x],x]==Cos[1/x]/x^2,{y[2/Pi]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2-\sin \left (\frac {1}{x}\right ) \]