69.17.10 problem 560

Internal problem ID [18346]
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 : 560
Date solved : Thursday, October 02, 2025 at 03:10:42 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x) = 18*x-10*cos(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.401 (sec). Leaf size: 51

ode=D[y[x],{x,2}]-3*D[y[x],x]==18*x-10*Cos[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]}2 e^{-3 K[1]} (9 K[1]-5 \cos (K[1]))dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-18*x + 10*cos(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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