Internal problem ID [1249]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = -1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
Order:=6; dsolve([(2-3*x+2*x^2)*diff(y(x),x$2)-(4-6*x)*diff(y(x),x)+2*y(x)=0,y(1) = 1, D(y)(1) = -1],y(x),type='series',x=1);
\[ y \relax (x ) = 1-\left (x -1\right )+\frac {4}{3} \left (x -1\right )^{3}-\frac {4}{3} \left (x -1\right )^{4}-\frac {4}{5} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[{(2-3*x+2*x^2)*y''[x]-(4-6*x)*y'[x]+2*y[x]==0,{y[1]==1,y'[1]==-1}},y[x],{x,1,5}]
\[ y(x)\to -\frac {4}{5} (x-1)^5-\frac {4}{3} (x-1)^4+\frac {4}{3} (x-1)^3-x+2 \]