74.16.14 problem 14

Internal problem ID [16520]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 09:10:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

With initial conditions

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

✓ Solution by Maple

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

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

\[ y = 3-2 x +\frac {5}{3} x^{2}-\frac {2}{9} x^{3}+\frac {1}{18} x^{4}+\frac {1}{135} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 36

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

\[ y(x)\to \frac {x^5}{135}+\frac {x^4}{18}-\frac {2 x^3}{9}+\frac {5 x^2}{3}-2 x+3 \]