Internal problem ID [1284]
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: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -3, y^{\prime }\relax (0) = 5] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(1+x^2)*diff(y(x),x$2)+(2+x^2)*diff(y(x),x)+x*y(x)=0,y(0) = -3, D(y)(0) = 5],y(x),type='series',x=0);
\[ y \relax (x ) = -3+5 x -5 x^{2}+\frac {23}{6} x^{3}-\frac {23}{12} x^{4}+\frac {11}{30} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{(1+x^2)*y''[x]+(2+x^2)*y'[x]+x*y[x]==0,{y[0]==-3,y'[0]==5}},y[x],{x,0,5}]
\[ y(x)\to \frac {11 x^5}{30}-\frac {23 x^4}{12}+\frac {23 x^3}{6}-5 x^2+5 x-3 \]