12.13.16 problem 19

Internal problem ID [1907]
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
Date solved : Monday, January 27, 2025 at 05:38:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-7 \end{align*}

Solution by Maple

Time used: 0.000 (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);
 
\[ y = 2-7 x -4 x^{2}-\frac {17}{6} x^{3}-\frac {3}{4} x^{4}-\frac {9}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 34

AsymptoticDSolveValue[{(2+4*x)*D[y[x],{x,2}]-4*D[y[x],x]-(6+4*x)*y[x]==0,{y[0]==2,Derivative[1][y][0] ==-7}},y[x],{x,0,"6"-1}]
 
\[ y(x)\to -\frac {9 x^5}{40}-\frac {3 x^4}{4}-\frac {17 x^3}{6}-4 x^2-7 x+2 \]