28.2.62 problem 62

Internal problem ID [4505]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 62
Date solved : Sunday, March 30, 2025 at 03:24:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=15 \,{\mathrm e}^{-x} \sqrt {1+x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 15*exp(-x)*(1+x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (4 \left (1+x \right )^{{5}/{2}}+c_1 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+2*D[y[x],x]+y[x]==15*Exp[-x]*Sqrt[1+x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (4 (x+1)^{5/2}+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.656 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-15*sqrt(x + 1)*exp(-x) + y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} - 6 x \sqrt {x + 1} + 10 \left (x + 1\right )^{\frac {3}{2}} - 2 \sqrt {x + 1}\right ) + 4 \sqrt {x + 1}\right ) e^{- x} \]