67.15.55 problem 22.11 (n)

Internal problem ID [16773]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.11 (n)
Date solved : Thursday, October 02, 2025 at 01:38:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 3*x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {72}{3125}+\left (c_1 x +c_2 \right ) {\mathrm e}^{5 x}+\frac {3 x^{4}}{25}+\frac {24 x^{3}}{125}+\frac {108 x^{2}}{625}+\frac {288 x}{3125} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 47

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==3*x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 \left (125 x^4+200 x^3+180 x^2+96 x+24\right )}{3125}+c_1 e^{5 x}+c_2 e^{5 x} x \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**4 + 25*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 x^{4}}{25} + \frac {24 x^{3}}{125} + \frac {108 x^{2}}{625} + \frac {288 x}{3125} + \left (C_{1} + C_{2} x\right ) e^{5 x} + \frac {72}{3125} \]