82.39.5 problem Ex. 5

Internal problem ID [18937]
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. 5
Date solved : Tuesday, January 28, 2025 at 12:37:28 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$3)+6*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} x^{3}+c_3 \ln \left (x \right )+c_{2}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_3 x^3+c_2 \log (x)+c_1}{x^2} \]