12.20.3 problem section 9.4, problem 11

Internal problem ID [2224]
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
Date solved : Monday, January 27, 2025 at 05:43:47 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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)
 

\[ y = \frac {2 x^{3} \ln \left (x \right )+6 c_3 \,x^{3}+6 c_2 \,x^{2}+c_1}{6 x} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {1}{3} x^2 \log (x)+\left (-\frac {4}{9}+c_3\right ) x^2+c_2 x+\frac {c_1}{x} \]