28.2.68 problem 68

Internal problem ID [4511]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 68
Date solved : Monday, January 27, 2025 at 09:22:31 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=9*x^2*ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} x \ln \left (x \right )+x c_3 +\frac {12 x^{3} \ln \left (x \right )-28 x^{3}+c_{1}}{4 x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 31

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==9*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -7 x^2+c_2 x+\frac {c_1}{x}+x (3 x+c_3) \log (x) \]