Internal problem ID [2404]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y \left (x +1\right )=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 69
Order:=6; dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*(1+x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1-4 x +4 x^{2}-\frac {16}{9} x^{3}+\frac {4}{9} x^{4}-\frac {16}{225} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (8 x -12 x^{2}+\frac {176}{27} x^{3}-\frac {50}{27} x^{4}+\frac {1096}{3375} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 116
AsymptoticDSolveValue[x^2*y''[x]-3*x*y'[x]+4*(1+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {16 x^5}{225}+\frac {4 x^4}{9}-\frac {16 x^3}{9}+4 x^2-4 x+1\right ) x^2+c_2 \left (\left (\frac {1096 x^5}{3375}-\frac {50 x^4}{27}+\frac {176 x^3}{27}-12 x^2+8 x\right ) x^2+\left (-\frac {16 x^5}{225}+\frac {4 x^4}{9}-\frac {16 x^3}{9}+4 x^2-4 x+1\right ) x^2 \log (x)\right ) \]