Internal problem ID [11307]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 55. Summary.
Page 129
Problem number: Ex 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x^{2}-4 y^{\prime } x +\left (x^{2}+6\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(6+x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 37
DSolve[x^2*y''[x]-4*x*y'[x]+(6+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-i x} x^2 \left (2 c_1-i c_2 e^{2 i x}\right ) \]