82.52.2 problem Ex. 2

Internal problem ID [19010]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 116
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:45:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 33

dsolve(4*x^2*diff(y(x),x$2)+4*x^5*diff(y(x),x)+( x^8+6*x^4+4)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \sqrt {x}\, {\mathrm e}^{-\frac {x^{4}}{8}} \left (c_{1} x^{\frac {i \sqrt {3}}{2}}+c_{2} x^{-\frac {i \sqrt {3}}{2}}\right ) \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 62

DSolve[4*x^2*D[y[x],{x,2}]+4*x^5*D[y[x],x]+( x^8+6*x^4+4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-\frac {x^4}{8}} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} \left (3 c_1-i \sqrt {3} c_2 x^{i \sqrt {3}}\right ) \]