# Recent questions in Differential equations

Differential equations

### $$\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}$$

Differential equations

### $$\displaystyle{d}^{{2}}\frac{{y}}{{\left.{d}{x}\right.}^{{2}}}−{2}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{10}{y}={0}$$ where $$x=0;y=0$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}?{x}={0};{y}={0}$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}$$?

Differential equations

### In many physical applications, the nonhomogeneous term F(x) is specified by different formulas in different intervals of x. (a) Find a general solution of the equation $$\displaystyle{y}{''}+{y}=\left\{{x},{0}\leq{x}\leq{1},{1}\leq{x}\right\}$$ NoteNote that the solution is not differentiable at x = 1. (b) Find a particular solution of $$y''+y=\left\{x,0\leq x\leq 1;1,1\leq x\right\}$$ that satises the initial conditions y(0)=0 and y′(0)=1.

Differential equations

### $$\displaystyle{2}⋅{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{2}{y}={0}$$

Differential equations

### Which is a narrow, debatable claim?

Differential equations

### You have a $150 gift card to use at a sporting goods store. You buy 2 pairs of shoes for$65. You plan to spend the rest of the money on socks. Socks cost \$4.75 per pair. What is the greatest number of pairs of socks you can purchase?

Differential equations

### When is the exponential population model appropriate? When is the logistic population model appropriate? When is an Allee model appropriate? Discuss the benets of each of these models and their drawbacks.

Differential equations

### If $$xy+8e^y=8e$$ , find the value of y" at the point where $$x=0$$ $$y"=?$$

Differential equations

### Solve the differential equation by variation of parameters $$y"+y=\sin x$$

Differential equations

### Solve the given differential equation by separation of variables: $$\frac{dP}{dt}=P-P^2$$

Differential equations

### A population like that of the United States with an age structure of roughly equal numbers in each of the age groups can be predicted to A) grow rapidly over a 30-year-period and then stabilize B) grow little for a generation and then grow rapidly C) fall slowly and steadily over many decades D) show slow and steady growth for some time into the future

Differential equations

### what is the squareroot of 2

Differential equations

### Find an equation of the tangent line to the curve at the given point (9, 3) $$y=\frac{1}{\sqrt{x}}$$

Differential equations

### $$\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{1}}+{x}+{x}^{{2}}$$. find the maclaurin polynomial

Differential equations

### Compute $$\triangle y$$ and dy for the given values of x and $$dx=\triangle x$$ $$y=x^2-4x, x=3 , \triangle x =0,5$$ $$\triangle y=???$$ dy=?

Differential equations

### Find equations of both lines through the point (2, ?3) that are tangent to the parabola $$y = x^2 + x$$. $$y_1$$=(smaller slope quation) $$y_2$$=(larger slope equation)

Differential equations

### The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. a) $$\int_{0}^{6}g(x)dx$$ b) $$\int_{6}^{18}g(x)dx$$ c) $$\int_{0}^{21}g(x)dx$$

Differential equations

### One property of Laplace transform can be expressed in terms of the inverse Laplace transform as $$L^{-1}\left\{\frac{d^nF}{ds^n}\right\}(t)=(-t)^n f(t)$$ where $$f=L^{-1}\left\{F\right\}$$. Use this equation to compute $$L^{-1}\left\{F\right\}$$ $$F(s)=\arctan \frac{23}{s}$$

Differential equations