Internal problem ID [1276]
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: 35.
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 (3 x^{2}+2\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -5] \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([diff(y(x),x$2)-2*x*diff(y(x),x)-(2+3*x^2)*y(x)=0,y(0) = 2, D(y)(0) = -5],y(x),type='series',x=0);
\[ y \relax (x ) = 2-5 x +2 x^{2}-\frac {10}{3} x^{3}+\frac {3}{2} x^{4}-\frac {25}{12} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{y''[x]-2*x*y'[x]-(2+3*x^2)*y[x]==0,{y[0]==2,y'[0]==-5}},y[x],{x,0,5}]
\[ y(x)\to -\frac {25 x^5}{12}+\frac {3 x^4}{2}-\frac {10 x^3}{3}+2 x^2-5 x+2 \]