7.10.49 problem 56

Internal problem ID [319]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 56
Date solved : Monday, January 27, 2025 at 02:43:36 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = c_3 \ln \left (x \right )^{2}+c_2 \ln \left (x \right )+c_1 \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 23

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

\[ y(x)\to \frac {1}{2} c_2 \log ^2(x)+c_1 \log (x)+c_3 \]