Internal problem ID [10273]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 14.
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 }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y-\frac {1}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
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)
\[ y \relax (x ) = c_{2} x \ln \relax (x )+x c_{3}+\frac {\ln \relax (x )+1+c_{1}}{4 x} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 33
DSolve[x^3*y'''[x]+2*x^2*y''[x]-x*y'[x]+y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \\ \end{align*}