separable differential equations

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

•  $\ln y=\frac{x^2}{2}+C$  

•  $y=\frac{x^2}{2}+C$  

•  $x^2=y^2+C$  

•  $y^2=x^2+2C$  

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.HSA.CED.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Solve the following differential equations:
 $\frac{\text{d}y}{\text{d}x}=3y$  

•  $y=Ce^{3x}$  

•  $y=3x+C$  

•  $\frac{y^2}{2}=3x+C$  

•  $\ln y=x+C$  

 $\frac{\text{d}y}{\text{d}x}=\frac{x}{y}$  

•  $y=\sqrt{x^2\ +c}$  

•  $\ln\ y\ =\ 0.5x^2\ +c$  

•  $y\ =\ 0.5x^2+c$  

•  $y\ =\ x^2+2c$  

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)

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.5