46.1.10 problem 16

Internal problem ID [7300]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page 174
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:49:55 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+4 y&=1 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

Order:=6; 
dsolve([diff(y(x),x)+4*y(x)=1,y(0) = 5/4],y(x),type='series',x=0);
 

\[ y = \frac {5}{4}-4 x +8 x^{2}-\frac {32}{3} x^{3}+\frac {32}{3} x^{4}-\frac {128}{15} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

AsymptoticDSolveValue[{D[y[x],x]+4*y[x]==1,{y[0]==125/100}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to -\frac {128 x^5}{15}+\frac {32 x^4}{3}-\frac {32 x^3}{3}+8 x^2-4 x+\frac {5}{4} \]