15.25.15 problem 14
Internal
problem
ID
[3402]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
43,
page
209
Problem
number
:
14
Date
solved
:
Monday, January 27, 2025 at 07:35:47 AM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=x^{2} \left (1+x \right )^{2} \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 61
Order:=6;
dsolve((2*x^2+x^3)*diff(y(x),x$2)-x*diff(y(x),x)+(1-x)*y(x)=x^2*(1+x)^2,y(x),type='series',x=0);
\[
y \left (x \right ) = c_{1} \sqrt {x}\, \left (1+\frac {5}{4} x +\frac {5}{96} x^{2}-\frac {11}{1152} x^{3}+\frac {341}{129024} x^{4}-\frac {20119}{23224320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (1+\frac {1}{3} x -\frac {1}{30} x^{2}+\frac {1}{126} x^{3}-\frac {11}{4536} x^{4}+\frac {19}{22680} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+x^{2} \left (\frac {1}{3}+\frac {1}{6} x +\frac {1}{126} x^{2}-\frac {11}{4536} x^{3}+\operatorname {O}\left (x^{4}\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 247
AsymptoticDSolveValue[(2*x^2+x^3)*D[y[x],{x,2}]-x*D[y[x],x]+(1-x)*y[x]==x^2*(1+x)^2,y[x],{x,0,"6"-1}]
\[
y(x)\to c_1 \sqrt {x} \left (-\frac {20119 x^5}{23224320}+\frac {341 x^4}{129024}-\frac {11 x^3}{1152}+\frac {5 x^2}{96}+\frac {5 x}{4}+1\right )+c_2 x \left (\frac {19 x^5}{22680}-\frac {11 x^4}{4536}+\frac {x^3}{126}-\frac {x^2}{30}+\frac {x}{3}+1\right )+\sqrt {x} \left (-\frac {20119 x^5}{23224320}+\frac {341 x^4}{129024}-\frac {11 x^3}{1152}+\frac {5 x^2}{96}+\frac {5 x}{4}+1\right ) \left (\frac {4997 x^{11/2}}{2903040}-\frac {1853 x^{9/2}}{181440}-\frac {183 x^{7/2}}{560}-\frac {5 x^{5/2}}{6}-\frac {2 x^{3/2}}{3}\right )+x \left (\frac {19 x^5}{22680}-\frac {11 x^4}{4536}+\frac {x^3}{126}-\frac {x^2}{30}+\frac {x}{3}+1\right ) \left (\frac {479 x^6}{136080}-\frac {13 x^5}{840}+\frac {13 x^4}{72}+\frac {17 x^3}{18}+\frac {3 x^2}{2}+x\right )
\]