9.2.25 problem problem 55

Internal problem ID [959]
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 55
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 }-x^{2} y^{\prime \prime }+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 35

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

\[ y(x)\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)+c_3 \]