62.32.6 problem Ex 6

Internal problem ID [12983]
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
Date solved : Tuesday, January 28, 2025 at 04:46:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = x^{2} \left (\sin \left (x \right ) c_{1} +\cos \left (x \right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(6+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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