Internal problem ID [14786]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
Order:=6; dsolve((1+3*x)*diff(y(x),x$2)-3*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+x^{2}+\frac {1}{6} x^{4}-\frac {1}{5} x^{5}\right ) y \left (0\right )+\left (x +\frac {3}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{30} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 52
AsymptoticDSolveValue[(1+3*x)*y''[x]-3*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{5}+\frac {x^4}{6}+x^2+1\right )+c_2 \left (\frac {x^5}{30}+\frac {x^3}{3}+\frac {3 x^2}{2}+x\right ) \]