Differential Equations - Separable Variable Method

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$  

• Separable.

• Non Separable

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=x^2y+x$  

• Separable.

• Non Separable.

The following Differential Equation is
 $x\frac{\text{d}y}{\text{d}x}=yx^2$  

• Separable.

• Non Separable.

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=y^2+xy^2$  

• Separable.

• Non Separable.

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=\frac{e^y}{e^x}$  

• Separable.

• Non Separable.

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

•  $y=Ax$  

•  $y^2=\ln x+C$  

•  $\ln y=\frac{x^2}{2}+C$  

•  $A=yx$  

Tags

CCSS.HSF.LE.A.4

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:
 $\frac{\text{d}y}{\text{d}x}=3y$  

•  $y=Ce^{3x}$  

•  $y=3x+C$  

•  $\frac{y^2}{2}=3x+C$  

•  $\ln y=x+C$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1