Internal problem ID [1283]
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: 41.
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^{2}+2 x +1\right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+(1+2*x+x^2)*diff(y(x),x)+2*y(x)=0,y(0) = 2, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \relax (x ) = 2+3 x -\frac {7}{2} x^{2}-\frac {5}{6} x^{3}+\frac {41}{24} x^{4}+\frac {41}{120} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[{y''[x]+(1+2*x+x^2)*y'[x]+2*y[x]==0,{y[0]==2,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {41 x^5}{120}+\frac {41 x^4}{24}-\frac {5 x^3}{6}-\frac {7 x^2}{2}+3 x+2 \]