Internal problem ID [15426]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 661.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }=\frac {x -1}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x$3)+diff(y(x),x$2)=(x-1)/x^3,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\int \int \frac {{\mathrm e}^{-x} \operatorname {expIntegral}_{1}\left (-x \right ) x^{2}-2 \,{\mathrm e}^{-x} c_{1} x^{2}+x -1}{x^{2}}d x d x \right )}{2}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 35
DSolve[y'''[x]+y''[x]==(x-1)/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \operatorname {ExpIntegralEi}(x)}{2}-\log (x)+c_1 e^{-x}+c_3 x+c_2 \]