85.61.5 problem 5

Internal problem ID [22859]
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 : 5
Date solved : Thursday, October 02, 2025 at 09:15:51 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 35

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

\[ y = x^{4}-4 x^{3}+12 x^{2}-{\mathrm e}^{-x} c_1 -\frac {{\mathrm e}^{2 x}}{3}-24 x +c_2 \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to x^4-4 x^3+12 x^2-24 x-\frac {e^{2 x}}{3}-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + x^{4} - 4 x^{3} + 12 x^{2} - 24 x - \frac {e^{2 x}}{3} \]