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Question: trying to solve a first order differential equation

Question:trying to solve a first order differential equation

vicky2811 25 Maple 2016
ode dsolve differential-equations
September 22 2021
2

 

 

 

 

 

"D1(s,t) :=P- (alpha1-beta*S) + alpha2 + beta2 *q(t)^();"

proc (s, t) options operator, arrow; P+beta*S-alpha1+alpha2+beta2*q(t) end proc

 (1)

"(->)"

dem

 (2)

``

ode1 := diff(q(t), t)+theta*q(t)/(1+N-t) = -D1(s, t)

diff(q(t), t)+theta*q(t)/(1+N-t) = -P-beta*S+alpha1-alpha2-beta2*q(t)

 (3)
> 

fn1 := q(t)

q(t)

 (4)
> 

ic1 := q(T) = 0

q(T) = 0

 (5)
> 

sol1 := simplify(dsolve({ic1, ode1}, fn1))

q(t) = (-S*beta-P+alpha1-alpha2)*(Int(exp(beta2*_z1)*(1+N-_z1)^(-theta), _z1 = T .. t))*exp(-beta2*t)*(1+N-t)^theta

 (6)

NULL

Download data.mw

Hello all. I'm trying to solve the following first-order differential equation. 

Please help in understanding why the equation (6) doesn't contain proper solution for the function q(t) on solving the ode1 with the given initial condition
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