Internal problem ID [5645]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-\frac {x -1}{x}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= \ln \relax (x ) \end {align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)+diff(y(x),x)=(x-1)/x,ln(x)],y(x), singsol=all)
\[ y \relax (x ) = \int \left ({\mathrm e}^{-x} \expIntegral \left (1, -x \right )+1+{\mathrm e}^{-x} c_{1}\right )d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 26
DSolve[y''[x]+y'[x]==(x-1)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (\text {ExpIntegralEi}(x)-c_1)+x-\log (x)+c_2 \\ \end{align*}