Question

一道要用微积分的数学题

我有一个作业是说一个人在打点滴，然后药在体内平均每升血是4 mg (L)-1 h-1 但是药在体内含量有浮动，是2sin（2pi*t/d） mg (L )-1 h-1（t是小时，L是每升血，H是每小时d是每天小时数（是24吧））然后人的肾脏每小时移除10%的药物（人有4L的血）问48小时后人体内的药物含量。提示：要用一道∫e^(kt)sin(jt) dt （k j是常数） 的式子我不奢求大家给我完整的答案（有就最好），但我希望大家能把你们知道的都告诉我。这100我肯定是会给的。我的翻译不是很好，下面给出原文：A patient is receiving a drug dissolved in a saline drip. Although the addition is continuous and at a constant average rate per unit volume of blood, there is a diurnal sinusoidal variation in the addition rate. Furthermore, the drug is removed by the patient's kidneys at a rate which is proportional to the concentration of the drug in the patient's blood.Derive and solve a differential equation describing the dependence on time of the drug concentration in the patient's blood. You can assume the volume of the patient's blood is a constant and that the rate of drug addition per unit volume of blood is a1 + a2sin(k1t), where a1, a2 and k1 are constants, and t is time.The patient's notes show that the average rate of addition of the drug is 4 mg (L blood)-1 h-1, and the diurnal variation around this average is given by 2sin mg (L blood)-1 h-1, where t is time in hours, and d is the number of hours in a day. The constant of proportionality for drug removal is 0.1 h-1, and the volume of blood is 4 L.What is the concentration of the drug in the patient's blood after 48 h, assuming there is no drug in the patient initially?

Answer 1

这就是求体内的药物残留啊，你会不会用matlab？
：a=input ('average rate:');
A=input('the amplitude of the diurnal variation');
k=input('the constant of proportionality for drug removal');t=input('time');
C =((a/k))*(1-exp(-k*t))+ (A/((pi/12)^2 + k^2))*((pi/12)*exp(-k*t) + k*sin((pi/12)*t)- (pi/12)*cos((pi/12)*t))
t=[0:48];
C =((a/k))*(1-exp(-k*t))+ (A/((pi/12)^2 + k^2))*((pi/12)*exp(-k*t) + k*sin((pi/12)*t)- (pi/12)*cos((pi/12)*t));
plot(t,C)
xlabel('Time (hours)')
ylabel('Concentration of Drug in the Blood')
title('Concentration of the drug in the first 48 hours')
貌似楼主没有分