Internal problem ID [1251]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.3 SERIES SOLUTIONS NEAR AN
ORDINARY POINT II. Exercises 7.3. Page 338
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (-4 x +1\right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = -1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 20
Order:=6; dsolve([(1-x+x^2)*diff(y(x),x$2)-(1-4*x)*diff(y(x),x)+2*y(x)=0,y(1) = 2, D(y)(1) = -1],y(x),type='series',x=1);
\[ y \relax (x ) = 2-\left (x -1\right )-\frac {1}{2} \left (x -1\right )^{2}+\frac {5}{3} \left (x -1\right )^{3}-\frac {19}{12} \left (x -1\right )^{4}+\frac {7}{30} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 44
AsymptoticDSolveValue[{(1-x+x^2)*y''[x]-(1-4*x)*y'[x]+2*y[x]==0,{y[1]==2,y'[1]==-1}},y[x],{x,1,5}]
\[ y(x)\to \frac {7}{30} (x-1)^5-\frac {19}{12} (x-1)^4+\frac {5}{3} (x-1)^3-\frac {1}{2} (x-1)^2-x+3 \]