85.67.2 problem 2

Internal problem ID [22893]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:16:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = {\mathrm e}^{2 x} c_1 +\frac {3 \cos \left (x \right )}{10}+\frac {\sin \left (x \right )}{10}+{\mathrm e}^{x} c_2 \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^x+c_2 e^{2 x}+\frac {1}{10} (\sin (x)+3 \cos (x)) \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + \frac {\sin {\left (x \right )}}{10} + \frac {3 \cos {\left (x \right )}}{10} \]