56.4.20 problem 20
Internal
problem
ID
[8909]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
4.0
Problem
number
:
20
Date
solved
:
Monday, January 27, 2025 at 05:19:07 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=1 \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✗ Solution by Maple
Order:=6;
dsolve(2*x^2*diff(y(x), x, x) + 2*x*diff(y(x), x) - x*y(x) = 1,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 360
AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-x*y[x]==1,y[x],{x,0,"6"-1}]
\[
y(x)\to c_2 \left (\frac {x^5}{460800}+\frac {x^4}{9216}+\frac {x^3}{288}+\frac {x^2}{16}+\frac {x}{2}+1\right )+c_1 \left (x^5 \left (\frac {\log (x)}{460800}-\frac {107}{13824000}\right )+x^4 \left (\frac {\log (x)}{9216}-\frac {19}{55296}\right )+x^3 \left (\frac {\log (x)}{288}-\frac {1}{108}\right )+x^2 \left (\frac {\log (x)}{16}-\frac {1}{8}\right )+x \left (\frac {\log (x)}{2}-\frac {1}{2}\right )+\log (x)+1\right )+\left (-\frac {137 x^6}{1990656000}+\frac {x^5}{4608000}+\frac {x^4}{73728}+\frac {x^3}{1728}+\frac {x^2}{64}+\frac {x}{4}+\frac {\log (x)}{2}\right ) \left (x^5 \left (\frac {\log (x)}{460800}-\frac {107}{13824000}\right )+x^4 \left (\frac {\log (x)}{9216}-\frac {19}{55296}\right )+x^3 \left (\frac {\log (x)}{288}-\frac {1}{108}\right )+x^2 \left (\frac {\log (x)}{16}-\frac {1}{8}\right )+x \left (\frac {\log (x)}{2}-\frac {1}{2}\right )+\log (x)+1\right )+\left (\frac {x^5}{460800}+\frac {x^4}{9216}+\frac {x^3}{288}+\frac {x^2}{16}+\frac {x}{2}+1\right ) \left (\frac {137 x^6 (6 \log (x)+5)}{11943936000}+\frac {x^5 (113-30 \log (x))}{138240000}+\frac {x^4 (41-12 \log (x))}{884736}+\frac {x^3 (3-\log (x))}{1728}+\frac {1}{128} x^2 (5-2 \log (x))+\frac {1}{4} x (2-\log (x))-\frac {1}{4} \log (x) (\log (x)+2)\right )
\]