# Recent questions in First order differential equations

First order differential equations

### Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt .

First order differential equations

### Write first-order differential equations that express the situation: A student in an engineering course finds the rate of increase of his grade point average GG is directly proportional to the number NN of study hours/week and inversely proportional to the amount AA of time spent on online games .

First order differential equations

### Identify the surface whose equation is given. $$\rho= \sin \theta \sin \phi$$

First order differential equations

### Write first-order differential equations that express the situation: A Walking Mode, l Construct a mathematical model to estimate how long it will take you to walk to the store for groceries. Suppose you have measured the distance as 11 mile and you estimate your walking speed as 33 miles per hour. If it takes you 2020 minutes to get to the store, what do you conclude about your model?

First order differential equations

### Write the following first-order differential equations in standard form. $$\displaystyle{y}'={x}^{{{3}}}{y}+{\sin{{x}}}$$

First order differential equations

### Find the differential of each function. (a) $$y = \tan \sqrt{t}$$ (b) $$y= \frac{1-v^2}{1+v^2}$$

First order differential equations

### Write the following first-order differential equations in standard form. $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={y}{x}{\left({x}+{1}\right)}$$

First order differential equations

### If $$f(x) + x^2[f(x)]^5 = 34$$ and $$f(1) = 2,$$ find $$f '(1).$$

First order differential equations

### How do you solve linear first-order differential equations?

First order differential equations

### Solve differential equation $$xy'+2y= -x^3+x, \ y(1)=2$$

First order differential equations

### Solve differential equation $$y '(t) = -3y + 9$$, $$y(0) = 4$$

First order differential equations

### Solve differential equation $$\frac{dy}{dx}+(\frac{a}{x})y=40x$$, for $$x>0$$ and $$y(1)=a$$

First order differential equations

### Solve differential equation $$\displaystyle{y}'+{y}={x},\ {y}{\left({0}\right)}={1}$$

First order differential equations

### Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}}}{{{y}}}},\ {y}{\left({0}\right)}=-{8}$$

First order differential equations

### Solve the differential equation $$y'-\lambda y= 1-\lambda t$$,  $$y(0)=0$$

First order differential equations

### Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\left({x}+{y}+{1}\right)}^{{2}}-{\left({x}+{y}-{1}\right)}^{{2}}$$

First order differential equations

### Solve differential equation $$xu'(x)= u^2-4$$

First order differential equations

### Solve differential equation $$(1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0$$

First order differential equations