Internal problem ID [1261]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x +2\right ) y^{\prime \prime }-y^{\prime } x +2 y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
Order:=6; dsolve([(2+3*x)*diff(y(x),x$2)-x*diff(y(x),x)+2*x*y(x)=0,y(0) = -1, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \relax (x ) = -1+2 x +\frac {1}{3} x^{3}-\frac {5}{12} x^{4}+\frac {2}{5} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 29
AsymptoticDSolveValue[{(2+3*x)*y''[x]-x*y'[x]+2*x*y[x]==0,{y[0]==-1,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to \frac {2 x^5}{5}-\frac {5 x^4}{12}+\frac {x^3}{3}+2 x-1 \]