Internal problem ID [6398]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 4(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime }=\frac {x -1}{x}} \] Given that one solution of the ode is \begin {align*} y_1 &= \ln \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)+diff(y(x),x)=(x-1)/x,ln(x)],y(x), singsol=all)
\[ y \left (x \right ) = \int \left (1+{\mathrm e}^{-x} \operatorname {Ei}_{1}\left (-x \right )+{\mathrm e}^{-x} c_{1} \right )d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 30
DSolve[y''[x]+y'[x]==(x-1)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \operatorname {ExpIntegralEi}(x)+x-\log (x)-c_1 e^{-x}+c_2 \]