75.6.18 problem 151

Internal problem ID [16774]
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
Date solved : Tuesday, January 28, 2025 at 09:22:08 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\infty \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.269 (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)
 

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

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 14

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

\[ y(x)\to \sin \left (\frac {1}{x}\right )+\cos \left (\frac {1}{x}\right ) \]