Differential Equations Jeopardy Template

Antiderivatives

General Solutions

Particular Solutions

Where did they go wrong?

100

Find the antiderivative for...

∫〖1/x〗dx

ln |x| + C

100

Find the general solution for...

dy/dx = (y+5)(x+2)

y = C₁e^{(x^2)/2 + 2x} - 5

100

Find the particular solution for...

y = C₁e^{(x^2)/2 + 2x} - 5

initial condition: f(0)=1

y = 5e^{(x^2)/2 + 2x} - 5

100

Slide 2

Step 1: She did not separate the variables correctly.

200

Find the antiderivative for...

∫〖secxtanx〗dx

secx + C

200

Find the general solution for...

dy/dx=y²(1+x²)

y= (-1)/(x+(x³/3)+C)

200

Find the particular solution for...

y= 〖-1〗/〖(1/6)x²+ C〗+ 2

initial condition: f(1)=0

y= 2-〖6/x²+2〗

200

Slide 4

Step 2: She forgot to add +C

300

Find the antiderivative for...

∫〖-1/|x|√ (x²-1)〗dx

cot^-1x + C

300

Find the general solution for...

dy/dx = 4x³y - 6x²y

Y = (+/-) C₁e^{(x^4)-(2x^3)}

300

Find the particular solution for...

y= (-3)/(3x+x³+C)

initial condition: f(3)=2

y= (-3)/(3x+x³-(75/2))

300

Slide 6

Step 3: A cube root does not include +/-

400

Find the antiderivavtive for...

∫〖cotx〗dx

ln|sinx| + C

400

Find the general solution for...

dy/dx= (3 - y)cosx

y=C₁e^-sinx+ 3

400

Find the particular solution for...

y=C₁e^-sinx + 3

initial condition: f(0)=1

y= 3 - 2e^-sinx

400

Slide 8

He is correct

500

Find the antiderivative for...

∫〖b^x〗

b^x/lnb + C

500

(2013 AP Exam Q) Find the general solution for...

dy/dx=e^y(3x²- 6x)

y= -ln(-x³+3x²+C)

500

(2010 AP Exam Q) Find the particular solution for...

y= (1)/(√-x² + C)

initial condition: f(1)=2

y= (1)/(√-x² + 5/4)

500

Slide 10

She is correct