Internal problem ID [6167]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots
Nonintegral. Exercises page 365
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 x y^{\prime \prime }+3 y^{\prime }+3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 52
Order:=8; dsolve(4*x*diff(y(x),x$2)+3*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{4}} \left (1-\frac {3}{5} x +\frac {1}{10} x^{2}-\frac {1}{130} x^{3}+\frac {3}{8840} x^{4}-\frac {3}{309400} x^{5}+\frac {3}{15470000} x^{6}-\frac {9}{3140410000} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1-x +\frac {3}{14} x^{2}-\frac {3}{154} x^{3}+\frac {3}{3080} x^{4}-\frac {9}{292600} x^{5}+\frac {9}{13459600} x^{6}-\frac {1}{94217200} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 111
AsymptoticDSolveValue[4*x*y''[x]+3*y'[x]+3*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \sqrt [4]{x} \left (-\frac {9 x^7}{3140410000}+\frac {3 x^6}{15470000}-\frac {3 x^5}{309400}+\frac {3 x^4}{8840}-\frac {x^3}{130}+\frac {x^2}{10}-\frac {3 x}{5}+1\right )+c_2 \left (-\frac {x^7}{94217200}+\frac {9 x^6}{13459600}-\frac {9 x^5}{292600}+\frac {3 x^4}{3080}-\frac {3 x^3}{154}+\frac {3 x^2}{14}-x+1\right ) \]