47.5.4 problem 4

Internal problem ID [7493]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:02:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }+x y^{\prime }-y&=\cos \left (\frac {1}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(x^3*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=cos(1/x),y(x), singsol=all)
 

\[ y = -\frac {x \left (-2 \,{\mathrm e}^{\frac {1}{x}} c_{2} +\cos \left (\frac {1}{x}\right )+\sin \left (\frac {1}{x}\right )-2 c_{1} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 32

DSolve[x^3*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==Cos[1/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} x \left (\sin \left (\frac {1}{x}\right )+\cos \left (\frac {1}{x}\right )-2 \left (c_1 e^{\frac {1}{x}}+c_2\right )\right ) \]