20.3 problem section 9.4, problem 11

Internal problem ID [1574]

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 11.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _exact, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 27

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

\[ y \relax (x ) = c_{2} x +x^{2} c_{3}+\frac {2 x^{3} \ln \relax (x )+c_{1}}{6 x} \]

Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 35

DSolve[x^3*y'''[x]+x^2*y''[x]-2*x*y'[x]+2*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} x^2 \log (x)+\left (-\frac {4}{9}+c_3\right ) x^2+c_2 x+\frac {c_1}{x} \\ \end{align*}