12.13.21 problem 24

Internal problem ID [1912]
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 : 24
Date solved : Monday, January 27, 2025 at 05:38:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

\begin{align*} -1 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

Order:=6; 
dsolve([(3+2*x)*diff(y(x),x$2)+3*diff(y(x),x)-x*y(x)=0,y(-1) = 2, D(y)(-1) = -3],y(x),type='series',x=-1);
 

\[ y = 2-3 \left (x +1\right )+\frac {7}{2} \left (x +1\right )^{2}-5 \left (x +1\right )^{3}+\frac {197}{24} \left (x +1\right )^{4}-\frac {287}{20} \left (x +1\right )^{5}+\operatorname {O}\left (\left (x +1\right )^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 44

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

\[ y(x)\to -\frac {287}{20} (x+1)^5+\frac {197}{24} (x+1)^4-5 (x+1)^3+\frac {7}{2} (x+1)^2-3 (x+1)+2 \]