Internal problem ID [1253]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = -2] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 20
Order:=6; dsolve([x^2*diff(y(x),x$2)-(6-7*x)*diff(y(x),x)+8*y(x)=0,y(1) = 1, D(y)(1) = -2],y(x),type='series',x=1);
\[ y \relax (x ) = 1-2 \left (x -1\right )-3 \left (x -1\right )^{2}+8 \left (x -1\right )^{3}-4 \left (x -1\right )^{4}-\frac {42}{5} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[{x^2*y''[x]-(6-7*x)*y'[x]+8*y[x]==0,{y[1]==1,y'[1]==-2}},y[x],{x,1,5}]
\[ y(x)\to -\frac {42}{5} (x-1)^5-4 (x-1)^4+8 (x-1)^3-3 (x-1)^2-2 (x-1)+1 \]