85.56.3 problem 1 (c)

Internal problem ID [22828]
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 199
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:15:28 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\[ y = \frac {x^{4}}{4}-\cos \left (x \right ) c_1 -3 x^{2}-\sin \left (x \right ) c_2 -2 \,{\mathrm e}^{x}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \frac {x^4}{4}-3 x^2-2 e^x+c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 32

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

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