DIFFERENTIAL EQUATIONS

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

• A) P=Ce^5t

  B) P= 5e^418t

• A) P=Ce^5t

  B) P= 418e^5t

• A) P=Ce^t

  B) P= 418e^t

• A) P=Ce^10t

  B) P= 418e^10t

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

• P=.05e^1000t

• P=1000e^5t

• P=1000e^.05t

• p=lne^1000t

Y is proportional to the difference of x and z

• y= x-z

• y= k(z-x)

• y= k(x-z)

• y= z-x

dy/dx = 2x/e^2y find the general solution

• y = ln (2x/2 + C)

  2

• y = ln(2x/2)+c

• y = e^2x+c

• y = mx+b

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

• 𝑦 = ln(15t)

• 𝑦 = 16t³

• 𝑦 = (2𝑡³ − 16)^1/2

• 𝑦 = (2𝑡³ −16)

dy/dx= x √y

Find the general solution

• √y = ln|4x| + c

• √y = (x)^-1 + c

• 2y^1/2 = ln|x| + c

• 1/2y^1/2 = ln|x| + c

y varies jointly with x and the square of z

• y= kxz²

• y= kx√z

• y= kxz

• kx²z

what would the sign of the square root after finding c be given the initial condition g(1)= -5

• positive

• negative

Dy/dx= tanx+15x2+e^x+1/x

• y= -ln|sinx| + 5x³ + e^x + ln|x| + c

• y= secxtanx + 5x³ + e^x + ln|x| + c

• y= -ln|cosx| + 5x³ + e^x + ln|x| + c

• y= sec²(x) + 5x³ + e^x + ln|x| + c

dp/dy = (4y)^-1find the general solution

• p= 1/5y^5/4 + c

• p= 1/4ln|4y| + c

• p= 1/8y² + c

• p= 1 + c

  4y