How to classify equilibrium points November 26    1

How to classify equilibrium points
I have the two differential equations:$$\frac{dN_1}{dt} = N_1(2 - N_1 - 2N_2)$$ $$\frac{dN_2}{dt} = N_2(3 - N_2 - 3N_1).$$I worked out the equilibrium points to be at $N_1 = 0, \frac{4}{5}$ ...

Compound Growth November 26    1

This is along the same lines as the population growth problem but a little more involved. I'm really lost on how to go about it. The question is: Suppose that each time a savings bank compounds the interest, you make an additional deposit $D(t)$. Sho

Getting wrong answer with reduction of order November 26    1

I always mess up reduction of order.$y''-4y'+4y=0$ has solution $y_1=e^{2x}$ using reduction of order $$y_2=y_1 \int \frac{e^{-\int{p(x)dx}}}{y_1^2}dx=e^{2x} \int \frac{e^{-(-4x)}}{(e^{2x})^2} dx=e^{2x} \cdot e^{2x}+C=e^{4x}+C$$but the answer key giv

reduction of order on nonhomogenious ODE November 26    1

Use reduction of order to find the homogeneous and associated particular solution. $y''-3y'+2y=5e^{3x}$ given $y_1=e^x$For homogeneous: $y_2=y_1 \int \frac{e^{-\int P(x) dx}}{y_1^2}dx=e^x \int \frac{e^3x}{e^2x} dx=e^{2x}$ Now what do I do?for a parti

Reduction of order and lost in arithmetic November 26    1

$4x^2y''+4xy'+(4x^)y=0, x>0, y_1(x)=\frac{1}{\sqrt(x)}sinx$Okay, I am so lost in the arithmetic of this problem. $y_2(x)= u(x)\frac{sinx}{\sqrt(x)}$ obviously, but I get so lost trying to find the next differential equation. I figure there's no po

Can you solve this Lagrange differential equation November 26    1

Can you solve this Lagrange differential equation
How can i found the solution for this: solve this using Lagrange method (differential equation): $$\color{red}{y=2y'x+y^3}$$ Hint: $$\color{#00F}{y^3 \equiv y'''}$$Can you explain the method ...

Streamlines tangent to velocity field November 26    1

As from the title, I'm not too sure how they are related. Definition is that streamlines are instantaneously tangential to the velocity vector of the field. Why would a steamline that shows direction be a tangent to the velocity? Thanks!The velocity

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