Internal problem ID [14777]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y=0} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
Order:=6; dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+7*y(x)=0,y(x),type='series',x=1);
\[ y \left (x \right ) = \left (1-\frac {7 \left (-1+x \right )^{2}}{2}+\frac {35 \left (-1+x \right )^{4}}{24}-\frac {7 \left (-1+x \right )^{5}}{6}\right ) y \left (1\right )+\left (-1+x +\left (-1+x \right )^{2}-\frac {5 \left (-1+x \right )^{3}}{6}+\frac {7 \left (-1+x \right )^{5}}{24}\right ) D\left (y \right )\left (1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 65
AsymptoticDSolveValue[x^2*y''[x]-2*x*y'[x]+7*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (-\frac {7}{6} (x-1)^5+\frac {35}{24} (x-1)^4-\frac {7}{2} (x-1)^2+1\right )+c_2 \left (\frac {7}{24} (x-1)^5-\frac {5}{6} (x-1)^3+(x-1)^2+x-1\right ) \]