Internal problem ID [4760]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.2.1 Exercises. page 290
Problem number: 7.2.102.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y x -\frac {1}{1-x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
Order:=6; dsolve([diff(y(x),x$2)-x*y(x)=1/(1-x),y(0) = 0, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = \frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{12} x^{4}+\frac {3}{40} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 56
AsymptoticDSolveValue[{y''[x]-x*y[x]==1/(1-x),{}},y[x],{x,0,5}]
\[ y(x)\to \frac {3 x^5}{40}+\frac {x^4}{12}+c_2 \left (\frac {x^4}{12}+x\right )+\frac {x^3}{6}+c_1 \left (\frac {x^3}{6}+1\right )+\frac {x^2}{2} \]