Internal problem ID [10907]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(x^2*diff(y(x),x$2)-4*x^2*diff(y(x),x)+(x^2+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x} \sqrt {x}\, \operatorname {BesselI}\left (\frac {i \sqrt {3}}{2}, \sqrt {3}\, x \right )+c_{2} {\mathrm e}^{2 x} \sqrt {x}\, \operatorname {BesselK}\left (\frac {i \sqrt {3}}{2}, \sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 67
DSolve[x^2*y''[x]-4*x^2*y'[x]+(x^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \sqrt {x} \left (c_1 \operatorname {BesselJ}\left (\frac {i \sqrt {3}}{2},-i \sqrt {3} x\right )+c_2 Y_{\frac {i \sqrt {3}}{2}}\left (-i \sqrt {3} x\right )\right ) \\ \end{align*}