Internal problem ID [1256]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)+3*x*diff(y(x),x)+(4+2*x^2)*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = 1-2 x^{2}+\frac {3}{2} x^{4}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 17
AsymptoticDSolveValue[{y''[x]+3*x*y'[x]+(4+2*x^2)*y[x]==0,{y[0]==1,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {3 x^4}{2}-2 x^2+1 \]