75.16.6 problem 479

Internal problem ID [16908]
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 : 479
Date solved : Monday, March 31, 2025 at 03:35:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (c_2 +c_1 x +\frac {1}{2} x^{2}\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{5 x} \left (x^2+2 c_2 x+2 c_1\right ) \]

✓ Sympy. Time used: 0.212 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - exp(5*x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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