78.12.32 problem 5 (h)

Internal problem ID [18319]
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 : 5 (h)
Date solved : Tuesday, January 28, 2025 at 11:46:13 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

\[ y = c_{1} x^{\sqrt {2}}+c_{2} x^{-\sqrt {2}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 28

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

\[ y(x)\to c_1 x^{-\sqrt {2}}+c_2 x^{\sqrt {2}} \]