Solving separable differential equations and using them in modeling

Practice Questions

AP Calculus AB › Solving separable differential equations and using them in modeling

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1

Find (dy/dx).

sin(xy) = x + cos(y)

2

Find the derivative:

3

Solve the separable differential equation:

$\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{4y}{x^2}, x>0$

and at

4

Given that and , solve for . What is the value of ?

5

If what is ?

6

Solve the separable differential equation:

$\frac{\mathrm{d} y}{\mathrm{d} x}=y\cos(x)$

given the condition at

$x=\pi, y=2$

7

Find the equation of the normal line at on the graph $y=x^{3}-6x+4$ .

8

Find $y^{'}$ if

$y=\frac{ln(x)}{x^{3}}$

9

Find the solution to the differential equation

$\frac{dy}{dx} = \frac{x^{2}+ 4x}{y^{2}}$ when .

10

is a function of . Solve for in this differential equation:

$\frac{\mathrm{d} y}{\mathrm{d} x} = \sqrt{\frac{ e^{y}}{x}}$

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