69.1.111 problem 158

Internal problem ID [14185]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 158
Date solved : Wednesday, March 05, 2025 at 10:39:09 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+5*diff(y(x),x)-2*y(x) = 2*x+3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_{2} +\left (c_{3} x +c_{1} \right ) {\mathrm e}^{x}-x -4 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 31

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+5*D[y[x],x]-2*y[x]==2*x+3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^x+x \left (-1+c_2 e^x\right )+c_3 e^{2 x}-4 \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x - 2*y(x) + 5*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{2 x} - x + \left (C_{1} + C_{2} x\right ) e^{x} - 4 \]