23.3.93 problem 95

Internal problem ID [5807]
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 : 95
Date solved : Tuesday, September 30, 2025 at 02:03:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=16*y(x)+8*diff(y(x),x)+diff(diff(y(x),x),x) = 4*exp(x)-exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-25 \,{\mathrm e}^{6 x}+144 \,{\mathrm e}^{5 x}+900 c_1 x +900 c_2 \right ) {\mathrm e}^{-4 x}}{900} \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 35

ode=16*y[x] + 8*D[y[x],x] + D[y[x],{x,2}] == 4*E^x - E^(2*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4 e^x}{25}-\frac {e^{2 x}}{36}+e^{-4 x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + exp(2*x) - 4*exp(x) + 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- 4 x} - \frac {e^{2 x}}{36} + \frac {4 e^{x}}{25} \]