85.61.4 problem 4

Internal problem ID [22858]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 208
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:15:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=2 x^{4}-3 x +1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)-y(x) = 2*x^4-3*x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{-x} c_1 -2 x^{4}-24 x^{2}+3 x -49 \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-y[x]==2*x^4-3*x+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -2 x^4-24 x^2+3 x+c_1 e^x+c_2 e^{-x}-49 \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**4 + 3*x - y(x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} - 2 x^{4} - 24 x^{2} + 3 x - 49 \]