Internal problem ID [14094]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}}} \] With initial conditions \begin {align*} \left [y \left (\frac {2}{\pi }\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([diff(y(x),x)=cos(1/x)/x^2,y(2/Pi) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\sin \left (\frac {1}{x}\right )+2 \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 13
DSolve[{y'[x]==Cos[1/x]/x^2,{y[2/Pi]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2-\sin \left (\frac {1}{x}\right ) \]