78.12.34 problem 7 (a)

Internal problem ID [18321]
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 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 7 (a)
Date solved : Tuesday, January 28, 2025 at 11:46:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(x*diff(y(x),x$2)+(x^2-1)*diff(y(x),x)+x^3*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x^{2}}{4}} \left (c_{1} \cos \left (\frac {x^{2} \sqrt {3}}{4}\right )+c_{2} \sin \left (\frac {x^{2} \sqrt {3}}{4}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 48

DSolve[x*D[y[x],{x,2}] +(x^2-1)*D[y[x],x]+x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {x^2}{4}} \left (c_2 \cos \left (\frac {\sqrt {3} x^2}{4}\right )+c_1 \sin \left (\frac {\sqrt {3} x^2}{4}\right )\right ) \]