Internal problem ID [6554]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y-\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)+y(x)=1/x,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 152
AsymptoticDSolveValue[y''[x]+y'[x]+y[x]==1/x,y[x],{x,0,5}]
\[ y(x)\to c_2 x \left (-\frac {x^4}{120}+\frac {x^3}{24}-\frac {x}{2}+1\right )+c_1 \left (\frac {x^3}{6}-\frac {x^2}{2}+1\right )+x \left (-\frac {x^4}{120}+\frac {x^3}{24}-\frac {x}{2}+1\right ) \left (\frac {41 x^6}{4320}+\frac {x^5}{120}-\frac {x^4}{96}-\frac {x^3}{18}+x+\log (x)\right )+\left (\frac {x^3}{6}-\frac {x^2}{2}+1\right ) \left (-\frac {x^6}{180}+\frac {x^5}{600}+\frac {x^4}{96}-\frac {x^2}{4}-x\right ) \]