Internal problem ID [1257]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -7] \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([(2+4*x)*diff(y(x),x$2)-4*diff(y(x),x)-(6+4*x)*y(x)=0,y(0) = 2, D(y)(0) = -7],y(x),type='series',x=0);
\[ y \relax (x ) = 2-7 x -4 x^{2}-\frac {17}{6} x^{3}-\frac {3}{4} x^{4}-\frac {9}{40} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{(2+4*x)*y''[x]-4*y'[x]-(6+4*x)*y[x]==0,{y[0]==2,y'[0]==-7}},y[x],{x,0,5}]
\[ y(x)\to -\frac {9 x^5}{40}-\frac {3 x^4}{4}-\frac {17 x^3}{6}-4 x^2-7 x+2 \]