Differential Equation

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

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

Tags

CCSS.HSA-REI.B.4B

Find the particular solution for y if dy/dx = 2x√y and y = 4 when x = 3.

• 2√y = x² + C

• y = (x² + 25)²/4

• y = (x²/2-5/2)^1/2

• y = x⁴/4

Tags

CCSS.HSA-REI.B.4B

Find the mistake if possible:

• The Diff EQ is solved correctly

• Step 1 is incorrect. The separation of variables wasn't done correctly.

• Step 2 is incorrect. They didn't integrate x² correctly.

• Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

Evaluate:

• 4

• 6

• 8

• 10

Of the following, which is a solution to the differential equation, select all that apply:
 $y''-6y'+8y=0$  

•  $y=2\sin\left(4x\right)$  

•  $y=3e^{2x}$  

•  $y=Ce^{4x},\$  where C is a constant

Is this a Linear Differential equation

• Yes

• No

• Maybe

• red

Solution of a linear differential equation of first order can be obtain by

• multiplying on both the sides by its integrating factor.

• adding on both the sides by integrating factor.

• subtracting integrating factor from both sides

• None of the above

What is the integrating factor for the differential equation:  $\frac{1}{x}\frac{\text{d}x}{\text{d}y}-\frac{1}{1+x^2}y=x^3$  

•  $\ln\left(x^2\right)$  

•  $-\frac{1}{x^2}$  

•  $-\frac{1}{\sqrt{x}}$  

•  $\frac{1}{\sqrt{x}}$  

The solution of linear differential equation  $x\frac{\text{d}y}{\text{d}x}+2y=x^2$  

•  $y=\frac{x^2+c}{4x^2}$  

•  $y=\frac{x^2}{4}+c$  

•  $y=\frac{x^4+c}{x^2}$  

•  $y=\frac{x^4+c}{4x^2}$