Internal problem ID [1254]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \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([(1+x+2*x^2)*diff(y(x),x$2)+(1+7*x)*diff(y(x),x)+2*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x),type='series',x=1);
\[ y \relax (x ) = 1-\frac {1}{4} \left (x -1\right )^{2}+\frac {13}{48} \left (x -1\right )^{3}-\frac {77}{384} \left (x -1\right )^{4}+\frac {287}{2560} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 41
AsymptoticDSolveValue[{(1+x+2*x^2)*y''[x]+(1+7*x)*y'[x]+2*y[x]==0,{y[1]==1,y'[1]==0}},y[x],{x,1,5}]
\[ y(x)\to \frac {287 (x-1)^5}{2560}-\frac {77}{384} (x-1)^4+\frac {13}{48} (x-1)^3-\frac {1}{4} (x-1)^2+1 \]