82.39.1 problem Ex. 1

Internal problem ID [18933]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:37:23 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-4/x*diff(y(x),x$2)+5/x^2*diff(y(x),x)-2/x^3*y(x)=1,y(x), singsol=all)
 

\[ y \left (x \right ) = x^{\frac {5}{2}+\frac {\sqrt {21}}{2}} c_3 +x^{\frac {5}{2}-\frac {\sqrt {21}}{2}} c_{2} -\frac {x^{2} \left (x +c_{1} \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 53

DSolve[D[y[x],{x,3}]-4/x*D[y[x],{x,2}]+5/x^2*D[y[x],x]-2/x^3*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{\frac {1}{2} \left (5+\sqrt {21}\right )}+c_1 x^{\frac {5}{2}-\frac {\sqrt {21}}{2}}-\frac {x^3}{5}+c_3 x^2 \]