Internal problem ID [2387]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (2+3 x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(2*x^2*diff(y(x),x$2)-3*(x+x^2)*diff(y(x),x)+(2+3*x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \sqrt {x}\, \left (1+\frac {3}{2} x +\frac {9}{8} x^{2}+\frac {9}{16} x^{3}+\frac {27}{128} x^{4}+\frac {81}{1280} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{2} \left (1+\frac {3}{5} x +\frac {9}{35} x^{2}+\frac {3}{35} x^{3}+\frac {9}{385} x^{4}+\frac {27}{5005} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 88
AsymptoticDSolveValue[2*x^2*y''[x]-3*(x+x^2)*y'[x]+(2+3*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {27 x^5}{5005}+\frac {9 x^4}{385}+\frac {3 x^3}{35}+\frac {9 x^2}{35}+\frac {3 x}{5}+1\right ) x^2+c_2 \left (\frac {81 x^5}{1280}+\frac {27 x^4}{128}+\frac {9 x^3}{16}+\frac {9 x^2}{8}+\frac {3 x}{2}+1\right ) \sqrt {x} \]