2016年10月13日 · Think of dy and dx each as discrete variables. So you could do something like multiply both sides by dx and end up with: iff dy=ydx And then divide both sides by y: iff …

2023年2月27日 · This is a standard example of separation of variables. First note that the zeros of the expression y(1-y) can give us constant solutions, depending on the value of y 0. If y=1 …

2018年4月4日 · The General Solution is: y = 1-1/(e^t + C) We have: dy/dt = e^t(y-1)^2 We can collect terms for similar variables: 1/(y-1)^2 \ dy/dt = e^t Which is a separable First Order …

2021年5月27日 · $\tiny{b.1.2.2a}$ $\dfrac{dy}{dt}=y-5, \quad y(0)=y_0$$\begin{array}{rll}\displaystyle y'&=y-5\\ y'-y&=-5\\ u(x)&=\exp\int-1\, dx&= e^{-t}\\...

2009年1月12日 · Homework Statement Find the general solution of the differential equation specified. \\frac{dy}{dt} = ty. The Attempt at a Solution I already know the answer to be …

2010年5月2日 · Homework Statement If dy/dt = ky and k is a nonzero constant, than y could be a. 2e^kty b. 2e^kt c. e^kt + 3 d. kty + 5 e. .5ky^2 + .5 Correct answer is b. 2e^kt Homework …

2008年3月4日 · First look at dy/dt= -y. That's easy to solve and gives the general solution to the associated "homogeneous equation". Now, try something of the form y= At+ B, for constants A …

2014年9月21日 · There are two values depending on the point. {dx}/{dt}={(-8 " at " (3,4)),(8 " at "(-3,4)):} Let us look at some details. First, let us find the values of x. By plugging in y=4 into …

2005年2月4日 · because dy = dt, then you will get a graph where a small change in y (within the y axis) will give an EQUIVALENT small change in t (in the t axis) i believe it is the same as …

2016年9月8日 · #(dy_h)/(dt)+3t y_h = 0# #(dy_p)/(dt)+3t y_p = sint# The homogeneous solution can be easily obtained. So grouping variables. #dy_h/y_h=-3tdt# giving. #y_h = C e^(-3/2t^2)# …