12.20.1 problem section 9.4, problem 3

Internal problem ID [2222]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 3
Date solved : Monday, January 27, 2025 at 05:43:45 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 26

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

\[ y = \frac {x \left (2 c_3 \,x^{2}+2 c_2 x +2 \ln \left (x \right )+2 c_1 +3\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 25

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

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