Internal problem ID [1273]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime } x +\left (2 x^{2}+3\right ) y=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: 0.001 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+2*x*diff(y(x),x)+(3+2*x^2)*y(x)=0,y(0) = 1, D(y)(0) = -2],y(x),type='series',x=0);
\[ y \relax (x ) = 1-2 x -\frac {3}{2} x^{2}+\frac {5}{3} x^{3}+\frac {17}{24} x^{4}-\frac {11}{20} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[{y''[x]+2*x*y'[x]+(3+2*x^2)*y[x]==0,{y[0]==1,y'[0]==-2}},y[x],{x,0,5}]
\[ y(x)\to -\frac {11 x^5}{20}+\frac {17 x^4}{24}+\frac {5 x^3}{3}-\frac {3 x^2}{2}-2 x+1 \]