Internal problem ID [13644]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.7 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y=0} \] 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(diff(y(x),x$2)+(1+2*x+6*x^2)*diff(y(x),x)+(2+12*x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}-\frac {5}{3} x^{3}+\frac {11}{12} x^{4}+\frac {101}{60} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{2}-\frac {1}{2} x^{3}-\frac {9}{8} x^{4}+\frac {41}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 68
AsymptoticDSolveValue[y''[x]+(1+2*x+6*x^2)*y'[x]+(2+12*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {101 x^5}{60}+\frac {11 x^4}{12}-\frac {5 x^3}{3}-x^2+1\right )+c_2 \left (\frac {41 x^5}{40}-\frac {9 x^4}{8}-\frac {x^3}{2}-\frac {x^2}{2}+x\right ) \]