38.4.15 problem 16

Internal problem ID [6501]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 16
Date solved : Wednesday, March 05, 2025 at 12:53:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+10*y(x) = 50*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 30

ode=D[y[x],{x,2}]+6*D[y[x],x]+10*y[x]==50*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 x+c_2 e^{-3 x} \cos (x)+c_1 e^{-3 x} \sin (x)-3 \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-50*x + 10*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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