15.12.15 problem 15

Internal problem ID [3159]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 15
Date solved : Sunday, March 30, 2025 at 01:19:58 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

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

\[ y = -{\mathrm e}^{-x} c_2 +\frac {{\mathrm e}^{4 x} c_1}{4}+\frac {3 \sin \left (x \right )}{34}-\frac {{\mathrm e}^{2 x}}{12}+\frac {5 \cos \left (x \right )}{34}+c_3 \]

✓ Mathematica. Time used: 0.285 (sec). Leaf size: 49

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

\[ y(x)\to -\frac {e^{2 x}}{12}+\frac {3 \sin (x)}{34}+\frac {5 \cos (x)}{34}+c_1 \left (-e^{-x}\right )+\frac {1}{4} c_2 e^{4 x}+c_3 \]

✓ Sympy. Time used: 0.283 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + C_{3} e^{4 x} - \frac {e^{2 x}}{12} + \frac {3 \sin {\left (x \right )}}{34} + \frac {5 \cos {\left (x \right )}}{34} \]