Internal problem ID [5072]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }+x y^{\prime }-y-\cos \left (\frac {1}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^3*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=cos(1/x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {1}{x}} x c_{2}+c_{1} x -\frac {x \left (\cos \left (\frac {1}{x}\right )+\sin \left (\frac {1}{x}\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 32
DSolve[x^3*y''[x]+x*y'[x]-y[x]==Cos[1/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}