Internal problem ID [2392]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (1+2 x \right ) y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
Order:=6; dsolve(4*x^2*(1-x)*diff(y(x),x$2)+3*x*(1+2*x)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \left (1-\frac {13}{4} x +\frac {117}{32} x^{2}-\frac {195}{128} x^{3}+\frac {195}{2048} x^{4}+\frac {117}{8192} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {3}{4}}}+c_{2} x \left (1-\frac {6}{11} x +\frac {4}{55} x^{2}+\frac {8}{1045} x^{3}+\frac {48}{24035} x^{4}+\frac {32}{43263} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 86
AsymptoticDSolveValue[4*x^2*(1-x)*y''[x]+3*x*(1+2*x)*y'[x]-3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (\frac {32 x^5}{43263}+\frac {48 x^4}{24035}+\frac {8 x^3}{1045}+\frac {4 x^2}{55}-\frac {6 x}{11}+1\right )+\frac {c_2 \left (\frac {117 x^5}{8192}+\frac {195 x^4}{2048}-\frac {195 x^3}{128}+\frac {117 x^2}{32}-\frac {13 x}{4}+1\right )}{x^{3/4}} \]