题目
题目

MTH1030 -1035 - S1 2025 MTH1030/35 Week 11 lesson quiz: Differential equations

简答题

What order differential equation is this: \(\frac{y'''+x\sqrt y}{yy'}=666 \)

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标准答案
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思路分析
To determine the order of a differential equation, identify the highest derivative of the unknown function y that appears in th......Login to view full explanation

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A cylindrical tank has a base radius of 5 cm and a height of 9 cm and is initially filled with water. The water flows out through a hole in the bottom of the tank at a rate of 5\( \sqrt[]{h} \)cm3/min, where h cm is the height of the water in the tank at time t. The time taken in minutes for the tank to empty is given by:

Question textThis is one of the problem sets that was part of the mock exam during COVID when the exam was fully online. There will be a problem set dedicated to differential equations on the real exam. However, that one will be hand-written. In general, to prepare for the differential equation part of the final exam, please make sure that you are familiar with the sample problems in the lecture notes and the applied class problem set.a) The differential equation with the initial condition y' = 2 x y, y(0) = 2has a solution of the form y(x) =What are c and d?Answer:c= Answer 1 Question 10[input]d= Answer 2 Question 10[input]b) A possible integrating factor for this differential equation y' + 3y/x = ex/x3is xc.What is c?Answer:c= Answer 3 Question 10[input]c) The differential equation y'' + 3 y' + 3 y = 6x+21has a particular solution of the form yp(x)=ax+b. What are a and b?Answer:a = Answer 4 Question 10[input]b = Answer 5 Question 10[input]

Question text 2Marks Let [math: y] be the solution to the initial value problem [math: x2dydx=ey and y(e)=1.]x^2\frac{dy}{dx}=e^{y}\ \text{ and }\ y(e)=1. Then the graph of [math: y] has an asymptote at [math: x=]Answer 5[input] and [math: y(1)=]Answer 6[input].Notes Report question issue Question 38 Notes

Consider the differential equation:  . If the general solution is      , which one of the following is the value of   ?

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