Internal problem ID [2258]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y=\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {4 c_{2} x^{2} \ln \left (x \right )+4 c_{3} x^{2}+\ln \left (x \right )+c_{1} +1}{4 x} \]
✓ Solution by Mathematica
Time used: 0.008 (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]
\[ y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \]