Internal problem ID [1242]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x +1\right ) y^{\prime \prime }+y^{\prime } x +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: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(1+3*x)*diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(0) = 2, D(y)(0) = -3],y(x),type='series',x=0);
\[ y \relax (x ) = 2-3 x -2 x^{2}+\frac {7}{2} x^{3}-\frac {55}{12} x^{4}+\frac {59}{8} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{(1+3*x)*y''[x]+x*y'[x]+2*y[x]==0,{y[0]==2,y'[0]==-3}},y[x],{x,0,5}]
\[ y(x)\to \frac {59 x^5}{8}-\frac {55 x^4}{12}+\frac {7 x^3}{2}-2 x^2-3 x+2 \]