78.9.13 problem 8

Internal problem ID [18261]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:44:40 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: 0.004 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(x^2+6)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 37

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

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