Internal problem ID [14808]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x y^{\prime \prime }+14 y^{\prime }+y \left (x -1\right )=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
Order:=6; dsolve(9*x*diff(y(x),x$2)+14*diff(y(x),x)+(x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \left (1+\frac {1}{4} x -\frac {3}{104} x^{2}-\frac {29}{6864} x^{3}+\frac {13}{65472} x^{4}+\frac {251}{11348480} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {5}{9}}}+c_{2} \left (1+\frac {1}{14} x -\frac {13}{644} x^{2}-\frac {59}{61824} x^{3}+\frac {29}{247296} x^{4}+\frac {53}{12364800} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 85
AsymptoticDSolveValue[9*x*y''[x]+14*y'[x]+(x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {53 x^5}{12364800}+\frac {29 x^4}{247296}-\frac {59 x^3}{61824}-\frac {13 x^2}{644}+\frac {x}{14}+1\right )+\frac {c_2 \left (\frac {251 x^5}{11348480}+\frac {13 x^4}{65472}-\frac {29 x^3}{6864}-\frac {3 x^2}{104}+\frac {x}{4}+1\right )}{x^{5/9}} \]