7.14.22 problem 22

Internal problem ID [447]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:53:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} -3 \end{align*}

With initial conditions

\begin{align*} y \left (-3\right )&=0\\ y^{\prime }\left (-3\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 9

Order:=6; 
dsolve([(x^2+6*x)*diff(y(x),x$2)+(3*x+9)*diff(y(x),x)-3*y(x)=0,y(-3) = 0, D(y)(-3) = 2],y(x),type='series',x=-3);
 

\[ y = 2 x +6 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 8

AsymptoticDSolveValue[{(x^2+6*x)*D[y[x],{x,2}]+(3*x+9)*D[y[x],x]-3*y[x]==0,{y[-3]==0,Derivative[1][y][-3] ==2}},y[x],{x,-3,"6"-1}]
 

\[ y(x)\to 2 (x+3) \]