Internal problem ID [1279]
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: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }+2 y^{\prime } x +\left (-x^{2}+4\right ) 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: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([3*diff(y(x),x$2)+2*x*diff(y(x),x)+(4-x^2)*y(x)=0,y(0) = -2, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \relax (x ) = -2+3 x +\frac {4}{3} x^{2}-x^{3}-\frac {19}{54} x^{4}+\frac {13}{60} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{3*y''[x]+2*x*y'[x]+(4-x^2)*y[x]==0,{y[0]==-2,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {13 x^5}{60}-\frac {19 x^4}{54}-x^3+\frac {4 x^2}{3}+3 x-2 \]