85.72.11 problem 2 (a)

Internal problem ID [22947]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 7. Solution of differential equations by use of series. A Exercises at page 316
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 09:16:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 76

Order:=6; 
ode:=2*diff(diff(y(x),x),x)-5*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x),type='series',x=1);
 

\[ y = \left (1-\frac {3 \left (x -1\right )^{2}}{4}-\frac {5 \left (x -1\right )^{3}}{8}-\frac {19 \left (x -1\right )^{4}}{64}-\frac {13 \left (x -1\right )^{5}}{128}\right ) y \left (1\right )+\left (x -1+\frac {5 \left (x -1\right )^{2}}{4}+\frac {19 \left (x -1\right )^{3}}{24}+\frac {65 \left (x -1\right )^{4}}{192}+\frac {211 \left (x -1\right )^{5}}{1920}\right ) y^{\prime }\left (1\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 87

ode=2*D[y[x],{x,2}]-5*D[y[x],x]+3*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,5}]
 

\[ y(x)\to c_1 \left (-\frac {13}{128} (x-1)^5-\frac {19}{64} (x-1)^4-\frac {5}{8} (x-1)^3-\frac {3}{4} (x-1)^2+1\right )+c_2 \left (\frac {211 (x-1)^5}{1920}+\frac {65}{192} (x-1)^4+\frac {19}{24} (x-1)^3+\frac {5}{4} (x-1)^2+x-1\right ) \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 65

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 5*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=1,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (x + \frac {65 \left (x - 1\right )^{4}}{192} + \frac {19 \left (x - 1\right )^{3}}{24} + \frac {5 \left (x - 1\right )^{2}}{4} - 1\right ) + C_{1} \left (- \frac {19 \left (x - 1\right )^{4}}{64} - \frac {5 \left (x - 1\right )^{3}}{8} - \frac {3 \left (x - 1\right )^{2}}{4} + 1\right ) + O\left (x^{6}\right ) \]