69.17.27 problem 577

Internal problem ID [18363]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 577
Date solved : Thursday, October 02, 2025 at 03:10:55 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x) = 1+exp(x)+cos(x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.345 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to \int _1^xe^{3 K[2]} \left (c_1+\int _1^{K[2]}e^{-3 K[1]} \left (\cos (K[1])+e^{K[1]}+\sin (K[1])+1\right )dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x) - sin(x) - cos(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{3 x} - \frac {x}{3} - \frac {e^{x}}{2} - \frac {\sqrt {2} \sin {\left (x + \frac {\pi }{4} \right )}}{10} + \frac {3 \sqrt {2} \cos {\left (x + \frac {\pi }{4} \right )}}{10} \]