82.45.3 problem Ex. 3

Internal problem ID [18971]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 100
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:41:06 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

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

\[ y \left (x \right ) = c_{1} +c_{2} x +c_3 \,x^{\frac {5}{2}+\frac {\sqrt {-4 a^{2}+1}}{2}}+c_4 \,x^{\frac {5}{2}-\frac {\sqrt {-4 a^{2}+1}}{2}} \]

✓ Solution by Mathematica

Time used: 0.447 (sec). Leaf size: 100

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

\[ y(x)\to -\frac {x^{\frac {1}{2} \left (5-\sqrt {\frac {1}{a^2}-4} a\right )} \left (\left (a^2+2 \sqrt {\frac {1}{a^2}-4} a-4\right ) c_2 x^{\sqrt {\frac {1}{a^2}-4} a}+\left (a^2-2 \sqrt {\frac {1}{a^2}-4} a-4\right ) c_1\right )}{a^4+8 a^2+12}+c_4 x+c_3 \]