Internal problem ID [6552]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 12.
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 {1}{x}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(diff(y(x),x$2)+diff(y(x),x)=1/x,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 159
AsymptoticDSolveValue[y''[x]+y'[x]==1/x,y[x],{x,0,5}]
\[ y(x)\to -\frac {x^6}{4320}-\frac {x^5}{600}-\frac {x^4}{96}-\frac {x^3}{18}-\frac {x^2}{4}+c_2 \left (-\frac {x^5}{720}+\frac {x^4}{120}-\frac {x^3}{24}+\frac {x^2}{6}-\frac {x}{2}+1\right ) x+\left (-\frac {x^5}{720}+\frac {x^4}{120}-\frac {x^3}{24}+\frac {x^2}{6}-\frac {x}{2}+1\right ) x \left (\frac {x^6}{2160}+\frac {x^5}{600}+\frac {x^4}{96}+\frac {x^3}{18}+\frac {x^2}{4}+x+\log (x)\right )-x+c_1 \]