Internal problem ID [2429]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y=x^{2} \left (x +2\right )^{2}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
Order:=6; dsolve((x^2+2*x)*diff(y(x),x$2)-(2+2*x)*diff(y(x),x)+2*y(x)=x^2*(x+2)^2,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{2} \left (1+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (-2-2 x -\frac {1}{2} x^{2}+\operatorname {O}\left (x^{6}\right )\right )+x^{3} \left (\frac {2}{3}+\frac {1}{6} x +\operatorname {O}\left (x^{3}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.317 (sec). Leaf size: 39
AsymptoticDSolveValue[(x^2+2*x)*y''[x]-(2+2*x)*y'[x]+2*y[x]==x^2*(x+2)^2,y[x],{x,0,5}]
\[ y(x)\to -\frac {1}{3} (x+1) x^3+\left (\frac {x^2}{2}+x\right ) x^2+c_2 x^2+c_1 (x+1) \]