62.32.3 problem Ex 3

Internal problem ID [12980]
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 3
Date solved : Tuesday, January 28, 2025 at 04:46:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2\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)+(2-x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sinh \left (x \right )+c_{2} \cosh \left (x \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 28

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

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