calculus
posted by jhony .
determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false
a) the function f(x)=3/2 +cx^2 is a solution of the differential equation xy'+2y=3
b) the differential equation dy/dx= (f(x)g(y))/ (F(x)+G(y) is separable.

a)
y=3/2 + c/x^2
y' = 2c/x^3
xy' + 2y = x(2c/x^3) + 2(3/2 + c/x^2)
= 2c/x^2 + 3 + 2c/x^2 = 3
b)
dy/dx = f(x)g(y)/(F(x)+G(y))
dy/g(y) (F(x)+G(y)) = f(x)dx
There's no way to separate the variables. That pesky F(x) is stuck fast to dy, or G(y) is stuck to dx.
Respond to this Question
Similar Questions

math
Algebra For questions 15, find the value of the variable. 1. x = (1 point) 2. y = (1 point) 3. x = (1 point) 4. x = (1 point) 5. (1 point) x = , y = , b = 90 x = , y = 3, b = 95 x = , y = 2, b = 90 x = , y = , b = 130 In Exercises … 
Chemistry: Answer check please!
1. Reactions follow the law of conservation of mass. a.) True b.) False Answer: True 2. Reactants are the materials used in a chemical reaction. a.) True b.) False Answer: True 3. In a chemical equation, the mass on the left of the … 
calculus
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. a if f is a function of x and y and a is a real number, then f(ax, ay)= af(x,y). b … 
7th grade health Ms. Sue please thanks
True/False Indicate whether the statement is true or false. 11. A person with good selfesteem is willing to try new things. (1 point) True False 12. Stress can be positive or negative. (1 point) True False 13. Giving away prized possessions … 
7th grade health true or false
11. Disagreements are a normal part of life. (1 point) True False 12. Talking to a trustworthy adult is the best way to stop sexual abuse and get help. (1 point) True False 13. Some conflicts are made worse by peer negotiation. (1 … 
Physical Ed
11. Disagreements are a normal part of life. (1 point) True False 12. Talking to a trustworthy adult is the best way to stop sexual abuse and get help. (1 point) True False 13. Some conflicts are made worse by peer negotiation. (1 … 
math
Indicate whether each statement is true or false by checking the appropriate box in the table below. a. 2x is a factor of the expression (2x + y ). True or False b. (2x + y ) is a factor of the expression 3(2x + y ). True or False … 
math
Indicate whether each statement is true or false by checking the appropriate box in the table below. a. 2x is a factor of the expression (2x + y ). True or False b. (2x + y ) is a factor of the expression 3(2x + y ). True or False … 
Calculus
Determine whether the statement is true or false. If it is false, give an example for which the statement fails. a) if f has a relative maximum at x0, then f(x0) is the largest value that f(x) can have 
Computer science
While you can pass only one argument into a function, you can return as many values as needed from a function. True False A library function saves time for the programmer because it allows for code reuse. True False Each function should …