11.1.2 Solving Separable Differential Equations Flashcards Preview

AP Calculus AB > 11.1.2 Solving Separable Differential Equations > Flashcards

Flashcards in 11.1.2 Solving Separable Differential Equations Deck (13):
1

Solving Separable Differential Equations

• To solve a separable differential equation, collect the x-terms with the dx differential and the y-terms with the dy differential.
• Initial conditions allow you to find a particular solution to a differential equation.

2

note

- Check whether this differential equation is separable.
Multiply both sides of the equation by dx.
- If you can gather all the x-terms with dx and all the y-terms with dy, then the differential equation is separable. You can then integrate each side of the equation.
- Each integral will have its own constant of integration, but you can combine them into a single constant C.
- This general solution can even be solved for y.
- Varying the value of the constant produces multiple solutions. You can graph them to form the solution curves.
- If you know the value of y corresponding to a given value of x, then you use can use this initial condition to determine a particular solution.
- When you plug in the values of x and y, the only unknown is C.
- Solve for C and plug it into the general solution to produce a particular solution.
- Multiply both sides of this differential equation by dx to
determine whether it is separable.
- It is separable, so integrate both sides.
- The two constants of integration combine to form one constant in the general solution. Varying the value of C produces a family of solution curves.
- General solutions do not always have to be solved for y.

3

Which of the following is a solution of dy/dx=y^2?

y=−1/x+1

4

Which of the following is the general solution of dy/dx=xe^x+y ?

–e^−y=xex−ex+C

5

Which of the following is the general solution of dydx=x/y^2+1 ?

x^2/2=y^3/3+y+C1

6

Which of the following is the general solution of 1/x^2+x dy/dx=y^−2?

y^3/3=x^3/3+x^2/2+C

7

Which of the following is the general solution of y2+y2x2+xdydx=1?

2x33+x22=y33+y22+C

8

Which of the following is the general solution of dydx=xy2y4+1 ?

x22=y33−1y+C

9

Which of the following is the general solution of dydx=xy?

y 2 = x 2 + C

10

Which of the following is the general solution of dydx=y2(x3+x2+1)?

−1y=x44+x33+x+C

11

Which of the following is the general solution of dydx=2xy2?

y=−1x2+C

12

Which of the following is the general solution of dydx=sinxy+1?

y22+y=C−cosx

13

Which of the following is the general solution of dydx=xy2−y2+x−1?

arctany=x22−x+C

Decks in AP Calculus AB Class (190):