7.13.22 problem 22

Internal problem ID [421]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:53:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+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 )&=1\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

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

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

\[ y = 1-2 x +2 x^{2}-\frac {4}{3} x^{3}+\frac {2}{3} x^{4}-\frac {4}{15} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to -\frac {4 x^5}{15}+\frac {2 x^4}{3}-\frac {4 x^3}{3}+2 x^2-2 x+1 \]