28.2.39 problem 39

Internal problem ID [4482]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 39
Date solved : Sunday, March 30, 2025 at 03:23:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=12 x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

ode:=diff(diff(y(x),x),x)-y(x) = 12*x^2*exp(x)+3*exp(2*x)+10*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\cos \left (3 x \right )+{\mathrm e}^{-x} c_1 +{\mathrm e}^{2 x}+\frac {\left (4 x^{3}-6 x^{2}+2 c_2 +6 x -3\right ) {\mathrm e}^{x}}{2} \]

✓ Mathematica. Time used: 0.323 (sec). Leaf size: 48

ode=D[y[x],{x,2}]-y[x]==12*x^2*Exp[x]+3*Exp[2*x]+10*Cos[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (2 x^3-3 x^2+3 x-\frac {3}{2}+c_1\right )+e^{2 x}-\cos (3 x)+c_2 e^{-x} \]

✓ Sympy. Time used: 0.154 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x**2*exp(x) - y(x) - 3*exp(2*x) - 10*cos(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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