Internal problem ID [1363]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
II. Exercises 7.6. Page 374
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 79
Order:=8; dsolve(9*x^2*(1+x)*diff(y(x),x$2)+3*x*(5+11*x-x^2)*diff(y(x),x)+(1+16*x-7*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-x +\frac {7}{6} x^{2}-\frac {23}{18} x^{3}+\frac {11}{8} x^{4}-\frac {1577}{1080} x^{5}+\frac {3319}{2160} x^{6}-\frac {72853}{45360} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+\left (-\frac {1}{12} x^{2}+\frac {13}{108} x^{3}-\frac {131}{864} x^{4}+\frac {11449}{64800} x^{5}-\frac {76919}{388800} x^{6}+\frac {4118557}{19051200} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) c_{2}}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 167
AsymptoticDSolveValue[9*x^2*(1+x)*y''[x]+3*x*(5+11*x-x^2)*y'[x]+(1+16*x-7*x^2)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to \frac {c_1 \left (-\frac {72853 x^7}{45360}+\frac {3319 x^6}{2160}-\frac {1577 x^5}{1080}+\frac {11 x^4}{8}-\frac {23 x^3}{18}+\frac {7 x^2}{6}-x+1\right )}{\sqrt [3]{x}}+c_2 \left (\frac {\frac {4118557 x^7}{19051200}-\frac {76919 x^6}{388800}+\frac {11449 x^5}{64800}-\frac {131 x^4}{864}+\frac {13 x^3}{108}-\frac {x^2}{12}}{\sqrt [3]{x}}+\frac {\left (-\frac {72853 x^7}{45360}+\frac {3319 x^6}{2160}-\frac {1577 x^5}{1080}+\frac {11 x^4}{8}-\frac {23 x^3}{18}+\frac {7 x^2}{6}-x+1\right ) \log (x)}{\sqrt [3]{x}}\right ) \]