37.3.4 problem 10.4.8 (d)

Internal problem ID [6410]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second order and Homogeneous. page 318
Problem number : 10.4.8 (d)
Date solved : Monday, January 27, 2025 at 02:00:53 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

\[ y = c_1 \sin \left (2 \sqrt {x}\, \sqrt {2}\right )+c_2 \cos \left (2 \sqrt {x}\, \sqrt {2}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 38

DSolve[x*D[y[x],{x,2}]+1/2*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (2 \sqrt {2} \sqrt {x}\right )+c_2 \sin \left (2 \sqrt {2} \sqrt {x}\right ) \]