88.27.5 problem 5

Internal problem ID [24235]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 226
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:01:08 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-7 y&=-x^{4}+2 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=a \\ \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 40

Order:=6; 
ode:=diff(y(x),x)-7*y(x) = -x^4+2; 
ic:=[y(0) = a]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = a +\left (7 a +2\right ) x +\left (\frac {49 a}{2}+7\right ) x^{2}+\left (\frac {343 a}{6}+\frac {49}{3}\right ) x^{3}+\left (\frac {2401 a}{24}+\frac {343}{12}\right ) x^{4}+\left (\frac {16807 a}{120}+\frac {2389}{60}\right ) x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 68

ode=D[y[x],{x,1}]-7*y[x]==2-x^4; 
ic={y[0]==a}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to \frac {1}{20} \left (14 a+\frac {2389}{6} (7 a+2)\right ) x^5+\frac {343}{24} (7 a+2) x^4+\frac {49}{6} (7 a+2) x^3+\frac {7}{2} (7 a+2) x^2+(7 a+2) x+a \]

✓ Sympy. Time used: 0.222 (sec). Leaf size: 60

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x**4 - 7*y(x) + Derivative(y(x), x) - 2,0) 
ics = {y(0): a} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

\[ y{\left (x \right )} = x \left (7 C_{1} + 2\right ) + \frac {7 x^{2} \left (7 C_{1} + 2\right )}{2} + \frac {49 x^{3} \left (7 C_{1} + 2\right )}{6} + \frac {343 x^{4} \left (7 C_{1} + 2\right )}{24} + \frac {x^{5} \left (16807 C_{1} + 4778\right )}{120} + C_{1} + O\left (x^{6}\right ) \]