Internal problem ID [2425]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 43, page 209
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y=x^{4}+x^{2}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 63
Order:=6; dsolve(9*x^2*diff(y(x),x$2)+(2+3*x)*y(x)=x^2+x^4,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}} \left (1-\frac {1}{2} x +\frac {1}{20} x^{2}-\frac {1}{480} x^{3}+\frac {1}{21120} x^{4}-\frac {1}{1478400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {2}{3}} \left (1-\frac {1}{4} x +\frac {1}{56} x^{2}-\frac {1}{1680} x^{3}+\frac {1}{87360} x^{4}-\frac {1}{6988800} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+x^{2} \left (\frac {1}{20}-\frac {3}{1120} x +\frac {1129}{123200} x^{2}-\frac {3387}{22422400} x^{3}+\operatorname {O}\left (x^{4}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 264
AsymptoticDSolveValue[9*x^2*y''[x]+(2+3*x)*y[x]==x^2+x^4,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (-\frac {x^5}{1478400}+\frac {x^4}{21120}-\frac {x^3}{480}+\frac {x^2}{20}-\frac {x}{2}+1\right )+x^{2/3} \left (-\frac {x^5}{6988800}+\frac {x^4}{87360}-\frac {x^3}{1680}+\frac {x^2}{56}-\frac {x}{4}+1\right ) \left (\frac {1057 x^{16/3}}{337920}-\frac {241 x^{13/3}}{6240}+\frac {21 x^{10/3}}{200}-\frac {x^{7/3}}{14}+\frac {x^{4/3}}{4}\right )+\sqrt [3]{x} \left (-\frac {x^5}{1478400}+\frac {x^4}{21120}-\frac {x^3}{480}+\frac {x^2}{20}-\frac {x}{2}+1\right ) \left (-\frac {223 x^{17/3}}{212160}+\frac {421 x^{14/3}}{23520}-\frac {57 x^{11/3}}{616}+\frac {x^{8/3}}{32}-\frac {x^{5/3}}{5}\right )+c_2 x^{2/3} \left (-\frac {x^5}{6988800}+\frac {x^4}{87360}-\frac {x^3}{1680}+\frac {x^2}{56}-\frac {x}{4}+1\right ) \]