Calculus - Diff EQs

dy/dx = 2x/e^2y find the general solution

• y = e^2x+c

• y = mx+b

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)

• √y = ln|4x| + c

• √y = (x)^-1 + c

• 2y^1/2 = ln|x| + c

• 1/2y^1/2 = ln|x| + c

what would the sign of the square root after finding c be given the initial condition g(1)= -5

• positive

• negative

dy/dx = (4x)^-1find the general solution

• y= 1/5x^5/4 + c

• y= 1/4ln|x| + c

• y= 1/8x² + c

• y= 1 + c

  4x

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

• B

• C

• D

• E

• 2

• -5

• -2

• 4

∫dx

• x+c

• 2x+c

• 3x+c

• 4x+c

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.

Find the Particular Solution