Internal problem ID [15044]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 151.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right )=-1} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x)*cos(1/x)-y(x)*sin(1/x)=-1,y(infinity) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\frac {1}{x}\right )+\cos \left (\frac {1}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 14
DSolve[{x^2*y'[x]*Cos[1/x]-y[x]*Sin[1/x]==-1,{y[Infinity]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin \left (\frac {1}{x}\right )+\cos \left (\frac {1}{x}\right ) \]