Internal problem ID [5426]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(6+9*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 37
DSolve[x^2*y''[x]-4*x*y'[x]+(6+9*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-3 i x} x^2 \left (6 c_1-i c_2 e^{6 i x}\right ) \]