75.16.41 problem 514

Internal problem ID [16943]
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. Trial and error method. Exercises page 132
Problem number : 514
Date solved : Monday, March 31, 2025 at 03:36:02 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=5*diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {3 x^{2}}{14}+\frac {25 \,{\mathrm e}^{\frac {7 x}{5}} c_1}{49}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 30

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]==3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3 x^2}{14}+c_3 x+\frac {1}{49} c_1 e^{7 x}+c_2 \]

✓ Sympy. Time used: 0.067 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*Derivative(y(x), (x, 2)) + 5*Derivative(y(x), (x, 3)) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{\frac {7 x}{5}} - \frac {3 x^{2}}{14} \]