Differential equations

Solve the differential equation.
 $\frac{dy}{dx}=\frac{2x}{y}$ 

•  $y=x+C$  

•  $y^2=x^2+C$  

•  $\frac{y^2}{2}=x^2+C$  

•  $y^2=x+C$  

Tags

CCSS.HSA-REI.B.4B

Solve the differential equation.
 $\frac{dy}{dt}=\frac{\sqrt{t}}{y^3}$ 

•  $\frac{y^4}{4}=t^{\frac{3}{2}}+C$  

•  $y=t^2+C$  

•  $y^3=t^2+C$  

•  $\frac{y^4}{4}=\frac{2}{3}t^{\frac{3}{2}}+C$  

Tags

CCSS.HSA-REI.B.4B

Solve the differential equation.
 $\frac{dy}{dx}=y^2$ 

•  $-\frac{1}{y}=x+C$  

•  $y=x+C$  

•  $y^3=x^2+C$  

•  $\frac{1}{y^2}=x+C$  

Solve the differential equation.
 $y'=\frac{-2x}{\sin y}$ 

•  $\cos y=-x^2+C$  

•  $-\cos y=-x^2+C$  

•  $\cos y=x+C$  

•  $\cos y=x^3+C$  

Solve the differential equation.
 $y'=x^2y$ 

•  $y=\frac{x^2}{2}+C$  

•  $\ln\left|y\right|=\frac{x^2}{2}+C$  

•  $\ln\left|y\right|=\frac{x^3}{3}+C$  

•  $\left|y\right|=x^2+C$  

Tags

CCSS.8.EE.C.8B

Solve the differential equation.
 $\frac{dy}{dx}=5y$  

Assume that y > 0

• 
   $y=Ce^{5x}$  

•  $\log y=5x+C$  

•  $y=5x+C$  

•  $y=x^2+C$