Internal problem ID [2381]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 41, page 195
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x \left (2+3 x \right ) y^{\prime \prime }-4 y^{\prime }+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
Order:=6; dsolve(3*x*(2+3*x)*diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {5}{3}} \left (1-\frac {7}{8} x +\frac {7}{8} x^{2}-\frac {23}{24} x^{3}+\frac {1817}{1632} x^{4}-\frac {219857}{163200} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (1+x -x^{2}+\frac {11}{12} x^{3}-\frac {319}{336} x^{4}+\frac {319}{300} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 79
AsymptoticDSolveValue[3*x*(2+3*x)*y''[x]-4*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {319 x^5}{300}-\frac {319 x^4}{336}+\frac {11 x^3}{12}-x^2+x+1\right )+c_1 \left (-\frac {219857 x^5}{163200}+\frac {1817 x^4}{1632}-\frac {23 x^3}{24}+\frac {7 x^2}{8}-\frac {7 x}{8}+1\right ) x^{5/3} \]