Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Differentiation - Differential Equations.
Test Yourself 1.


 
1. If y = 3e-2x, show that

2. If y = e2x + e4x, show that

3. Given that y = xe-2x, prove that

4. If y = x2 e3x, show that

5. Given that y = ekx is a solution of the equation y " - y ' - 6y = 0, find the value(s) of k. 6. If y = e3x, and

find the value of a.
7. The function y = e-kx satisfies the equation .

Show that k2 - 4k + 3 = 0.

 8. Consider the function

y = (x2 + 1)e-x.

(i) Find the first and second derivatives of this function.

(ii) If ,
find values for a and b.
9. If y = A cos4x + Bsin 4x, show that:

 
11. 12.