







f(x) + f ''''(x)=0 
20130305 

Andreea pose la question : Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something. Brennan Yaremko lui répond. 





Separating variables 
20081104 

Terry pose la question : by separating variables solve the initial value problem
(x+1)y' + y = 0 y(0) = 1 Harley Weston lui répond. 





A series solution of y' = xy 
20080703 

sasha pose la question : I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks Harley Weston lui répond. 





The rate of change of the concentration of a solution 
20071030 

Nicholas pose la question : A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the wellmixed salt water solution flow out at the same rate, how much salt is present after 8 minutes?
I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks Harley Weston lui répond. 





Solve y'' + y = 0 
20070728 

Shihya pose la question : How do you solve y’’ + y = 0 Stephen La Rocque and Harley Weston lui répond. 





What is the intensity 5m below the surface? 
20070331 

david pose la question : I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Penny Nom lui répond. 





U'(X)  U(X) = 0; U(0) = 2 
20050923 

David pose la question : Out of interest could you please answer the following questions?
U'(X)  U(X) = 0; U(0) = 2
and
U''(X)  U'(X) = 0; U'(0) = U(0) = 2
Harley Weston lui répond. 





An ODE 
20041110 

David pose la question : I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Harley Weston lui répond. 





The integrating factor method 
20040805 

A student pose la question : Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Harley Weston lui répond. 





Undetermined coefficients 
20011122 

Hoda pose la question : The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Harley Weston lui répond. 





A mixture problem 
20000306 

Rebecca Edwards pose la question : A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t. Harley Weston lui répond. 

