Internal problem ID [1282]
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: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }+y^{\prime } x^{2}+\left (1+2 x \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: 0.001 (sec). Leaf size: 20
Order:=6; dsolve([(1+x)*diff(y(x),x$2)+x^2*diff(y(x),x)+(1+2*x)*y(x)=0,y(0) = -2, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \relax (x ) = -2+3 x +x^{2}-\frac {1}{6} x^{3}-\frac {3}{4} x^{4}+\frac {31}{120} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[{(1+x)*y''[x]+x^2*y'[x]+(1+2*x)*y[x]==0,{y[0]==-2,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {31 x^5}{120}-\frac {3 x^4}{4}-\frac {x^3}{6}+x^2+3 x-2 \]