Math Help - Show a solution satisfies the DE

1. Show a solution satisfies the DE

hey . i need the solution :

1- y‘= 1+y^2 . y= tan (x+c)

2- y‘‘+2y‘+10y=0 . y= a cos pi x + b sin pi x

3- y‘‘‘= cos x . y= - sin x + ax^2 + bx + c

2. Originally Posted by hpla
hey . i need the solution :

1- y‘= 1+y^2 . y= tan (x+c)
I don't understand this format. You are given a D.E and the answer? In this case y= tan (x+c), so find y' and see if it satisfies the D.E. Or do you have to solve the D.E. showing y= tan (x+c)?

3. Also, show some work!
Does the question read "verify if y is a solutions for the given DE"???

4. Originally Posted by TheChaz
Also, show some work!
Does the question read "verify if y is a solutions for the given DE"???
how i get y‘ for :

y= a cos pi x + b sin pi x

y= - sin x + ax^2 + bx + c

. y= tan (x+c)

5. For the first, use the chain rule and knowledge of trig functions.
[a cos pi x]' = -pi*a sin pi x
etc
Have you taken Calculus?