Internal problem ID [2431]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y=x^{2} \left (x +1\right )^{2}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
Order:=6; dsolve((2*x^2+x^3)*diff(y(x),x$2)-x*diff(y(x),x)+(1-x)*y(x)=x^2*(1+x)^2,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \sqrt {x}\, \left (1+\frac {5}{4} x +\frac {5}{96} x^{2}-\frac {11}{1152} x^{3}+\frac {341}{129024} x^{4}-\frac {20119}{23224320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (1+\frac {1}{3} x -\frac {1}{30} x^{2}+\frac {1}{126} x^{3}-\frac {11}{4536} x^{4}+\frac {19}{22680} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+x^{2} \left (\frac {1}{3}+\frac {1}{6} x +\frac {1}{126} x^{2}-\frac {11}{4536} x^{3}+\operatorname {O}\left (x^{4}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.273 (sec). Leaf size: 247
AsymptoticDSolveValue[(2*x^2+x^3)*y''[x]-x*y'[x]+(1-x)*y[x]==x^2*(1+x)^2,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (-\frac {20119 x^5}{23224320}+\frac {341 x^4}{129024}-\frac {11 x^3}{1152}+\frac {5 x^2}{96}+\frac {5 x}{4}+1\right )+c_2 x \left (\frac {19 x^5}{22680}-\frac {11 x^4}{4536}+\frac {x^3}{126}-\frac {x^2}{30}+\frac {x}{3}+1\right )+\sqrt {x} \left (-\frac {20119 x^5}{23224320}+\frac {341 x^4}{129024}-\frac {11 x^3}{1152}+\frac {5 x^2}{96}+\frac {5 x}{4}+1\right ) \left (\frac {4997 x^{11/2}}{2903040}-\frac {1853 x^{9/2}}{181440}-\frac {183 x^{7/2}}{560}-\frac {5 x^{5/2}}{6}-\frac {2 x^{3/2}}{3}\right )+x \left (\frac {19 x^5}{22680}-\frac {11 x^4}{4536}+\frac {x^3}{126}-\frac {x^2}{30}+\frac {x}{3}+1\right ) \left (\frac {479 x^6}{136080}-\frac {13 x^5}{840}+\frac {13 x^4}{72}+\frac {17 x^3}{18}+\frac {3 x^2}{2}+x\right ) \]