28.2.14 problem 14

Internal problem ID [4457]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 14
Date solved : Sunday, March 30, 2025 at 03:23:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x)-8*diff(y(x),x)+17*y(x) = exp(4*x)*(x^2-3*sin(x)*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\left (3 x^{2}+4 c_1 \right ) \cos \left (x \right )+\left (-3 x +4 c_2 \right ) \sin \left (x \right )+4 x^{2}-8\right ) {\mathrm e}^{4 x}}{4} \]

✓ Mathematica. Time used: 0.235 (sec). Leaf size: 47

ode=D[y[x],{x,2}]-8*D[y[x],x]+17*y[x]==Exp[4*x]*(x^2-3*x*Sin[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} e^{4 x} \left (8 \left (x^2-2\right )+\left (6 x^2-3+8 c_2\right ) \cos (x)+(-6 x+8 c_1) \sin (x)\right ) \]

✓ Sympy. Time used: 0.547 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**2 + 3*x*sin(x))*exp(4*x) + 17*y(x) - 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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