Differential Equations

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

• $y=\ln\left|15t\right|$

• $y=16t^3$

• $y\ =\ \sqrt{2t^3-16}$

• $y=2t^3-16$

Determine the value of "c" that satisfies the differential equation  $\frac{dy}{dx}=\frac{x+1}{y+2}$  if the curve goes through the point (0, -1).

• 5/2

• -3/2

• -1/2

• 1

Which of the following is the solution to the differential equation  $\frac{dy}{dx}=\frac{x^2}{y}$  with the initial condition y(3) = -2?

•  $y=-2e^{\left(-9+\frac{x^3}{3}\right)}$  

•  $y=\sqrt{\frac{2x^3}{3}}$  

•  $y=\sqrt{\frac{2x^3}{3}-14}$  

•  $y=-\sqrt{\frac{2x^3}{3}-14}$  

Tags

CCSS.HSA.SSE.A.1

CCSS.HSN.RN.A.2

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

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Solve the following differential equations:
 $\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$  

•  $\sin y=1+C$  

•  $\sin y=x+C$  

•  $-\sin y=\frac{x^2}{2}+C$  

•  $\sin y=0+C$  

Tags

CCSS.HSF.TF.B.7

Solve the following differential equations:
 $\frac{\text{d}y}{\text{d}x}=e^x$  

•  $1=e^x+C$  

•  $y=\frac{e^x}{2}+C$  

•  $y=e^x+C$  

•  $0=e^x+C$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSA.CED.A.1

Let $\frac{dy}{dx}=-0.4y$ and  $y=5\$  when  $x=0$  .  

What is the solution for  $y$  ?

•  $y=5e^{-0.4x}$  

•  $y=-0.4e^{5x}$  

•  $y=5e^{-\frac{x}{0.4}}$  

•  $y=0.4e^{\frac{x}{5}}$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

CCSS.HSF.BF.A.1

Solve the differential equation $\frac{dy}{dt}=\frac{3t^2}{y}$   with initial condition 𝑦(2) = 0.

• 𝑦 = ln(15t)

• 𝑦 = 16t³

• 𝑦 = (2𝑡³ − 16)^1/2

• 𝑦 = (2𝑡³ −16)