Internal problem ID [5458]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 25. Integration in series. Supplemetary problems. Page 205
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y x^{2}=x^{2}+x +1} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
Order:=6; dsolve(diff(y(x),x$2)+x^2*y(x)=1+x+x^2,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {x^{4}}{12}\right ) y \left (0\right )+\left (x -\frac {1}{20} x^{5}\right ) D\left (y \right )\left (0\right )+\frac {x^{2}}{2}+\frac {x^{3}}{6}+\frac {x^{4}}{12}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]+x^2*y[x]==1+x+x^2,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^5}{20}\right )+\frac {x^4}{12}+c_1 \left (1-\frac {x^4}{12}\right )+\frac {x^3}{6}+\frac {x^2}{2} \]