15.16.9 problem 9

Internal problem ID [3229]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:26:51 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&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=1/x,y(x), singsol=all)
 

\[ y = \frac {4 c_2 \,x^{2} \ln \left (x \right )+4 c_3 \,x^{2}+\ln \left (x \right )+c_{1} +1}{4 x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 33

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
 

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