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 : Wednesday, March 05, 2025 at 04:22:53 AM
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*}

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

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

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

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

ode=D[y[x],x]+4*y[x]==1; 
ic={y[0]==125/100}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.734 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + Derivative(y(x), x) - 1,0) 
ics = {y(0): 5/4} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

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