9.2.24 problem problem 54

Internal problem ID [958]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 54
Date solved : Monday, January 27, 2025 at 03:22:38 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = c_1 +c_2 \ln \left (x \right )+\frac {c_3}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

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

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