Internal problem ID [1224]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = -2, y^{\prime }\relax (3) = 3] \end {align*}
With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+(x-3)*diff(y(x),x)+3*y(x)=0,y(3) = -2, D(y)(3) = 3],y(x),type='series',x=3);
\[ y \relax (x ) = -2+3 \left (x -3\right )+3 \left (x -3\right )^{2}-2 \left (x -3\right )^{3}-\frac {5}{4} \left (x -3\right )^{4}+\frac {3}{5} \left (x -3\right )^{5}+\mathrm {O}\left (\left (x -3\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[{y''[x]+(x-3)*y'[x]+3*y[x]==0,{y[3]==-2,y'[3]==3}},y[x],{x,3,5}]
\[ y(x)\to \frac {3}{5} (x-3)^5-\frac {5}{4} (x-3)^4-2 (x-3)^3+3 (x-3)^2+3 (x-3)-2 \]