23.3.79 problem 81

Internal problem ID [5793]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 81
Date solved : Tuesday, September 30, 2025 at 02:03:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=10 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=-4*y(x)-3*diff(y(x),x)+diff(diff(y(x),x),x) = 10*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 38

ode=-4*y[x] - 3*D[y[x],x] + D[y[x],{x,2}] == 10*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3}{5} \sin (2 x)-\frac {4}{5} \cos (2 x)+c_1 e^{-x}+c_2 e^{4 x} \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 10*cos(2*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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