Internal problem ID [14804]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y \left (x^{2}-1\right )=0} \] 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((x^2-3*x-4)*diff(y(x),x$2)-(x+1)*diff(y(x),x)+(x^2-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{8} x^{2}+\frac {1}{24} x^{3}+\frac {1}{192} x^{4}-\frac {1}{640} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{8} x^{2}-\frac {1}{24} x^{3}+\frac {1}{48} x^{4}+\frac {1}{960} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(x^2-3*x-4)*y''[x]-(x+1)*y'[x]+(x^2-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{640}+\frac {x^4}{192}+\frac {x^3}{24}-\frac {x^2}{8}+1\right )+c_2 \left (\frac {x^5}{960}+\frac {x^4}{48}-\frac {x^3}{24}-\frac {x^2}{8}+x\right ) \]