Internal problem ID [2382]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (4+x \right ) y^{\prime \prime }+7 y^{\prime } x -y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
Order:=6; dsolve(x^2*(4+x)*diff(y(x),x$2)+7*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {5}{4}} \left (1+\frac {1}{48} x -\frac {5}{19968} x^{2}+\frac {25}{1810432} x^{3}-\frac {75}{62390272} x^{4}+\frac {39}{293601280} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1+2 x +\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 58
AsymptoticDSolveValue[x^2*(4+x)*y''[x]+7*x*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [4]{x} \left (\frac {39 x^5}{293601280}-\frac {75 x^4}{62390272}+\frac {25 x^3}{1810432}-\frac {5 x^2}{19968}+\frac {x}{48}+1\right )+\frac {c_2 (2 x+1)}{x} \]