Internal problem ID [2428]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y=6 \left (-x^{2}+1\right )^{2}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
Order:=6; dsolve((1-x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=6*(1-x^2)^2,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (x^{2}+1\right ) y \left (0\right )-x^{4}+D\left (y \right )\left (0\right ) x +3 x^{2}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 26
AsymptoticDSolveValue[(1-x^2)*y''[x]+2*x*y'[x]-2*y[x]==6*(1-x^2)^2,y[x],{x,0,5}]
\[ y(x)\to -x^4+3 x^2+c_1 \left (x^2+1\right )+c_2 x \]