Internal problem ID [1248]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 5] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(4+x)*diff(y(x),x$2)+(2+x)*diff(y(x),x)+2*y(x)=0,y(0) = 2, D(y)(0) = 5],y(x),type='series',x=0);
\[ y \relax (x ) = 2+5 x -\frac {7}{4} x^{2}-\frac {3}{16} x^{3}+\frac {37}{192} x^{4}-\frac {7}{192} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[{(4+x)*y''[x]+(2+x)*y'[x]+2*y[x]==0,{y[0]==4,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to -\frac {7 x^5}{192}+\frac {25 x^4}{192}+\frac {x^3}{16}-\frac {7 x^2}{4}+3 x+4 \]