Internal problem ID [14787]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (-x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } \left (x -1\right )+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((2-x^2)*diff(y(x),x$2)+2*(x-1)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}-\frac {1}{3} x^{3}+\frac {1}{6} x^{4}+\frac {1}{15} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}-\frac {5}{24} x^{4}-\frac {1}{120} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 68
AsymptoticDSolveValue[(2-x^2)*y''[x]+2*(x-1)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{15}+\frac {x^4}{6}-\frac {x^3}{3}-x^2+1\right )+c_2 \left (-\frac {x^5}{120}-\frac {5 x^4}{24}-\frac {x^3}{3}+\frac {x^2}{2}+x\right ) \]