# Tutor profile: Paul G.

## Questions

### Subject: Calculus

Solve for the second derivative of the following equation: f(x) = (x + 2)^2 + 2x + 3

Solve for derivatives: f(x) = x^2 + 4x + 4 + 2x + 3 = x^2 + 6x + 7 f’(x) = 2x + 6 f”(x) = 2

### Subject: Differential Equations

Solve the second order differential equation: d^2y/dx + 2 dy/dx + y = 2x -6

First solve the homogeneous solution (yh) of the auxiliary equation rewritten as: m^2 + 2 m + 1 = 0 (m + 1)*(m + 1) = 0 Real root: m = -1 repeated Therefore yh = C1*e^-x + C2*x*e^-x Then solve for the particular solution (yp) and substitute into the differential equation as shown below: yp = Ax + B yp’ = A yp” = 0 yp” + 2yp’ + yp = 2 x + 4 0 + 2A + Ax + B = 2x + 4 x: Ax = 2x (A =2) constant: 2A + B = 4, 2(2) +B = 4 (B = 0) So, yp = 2x y = yh + yp therefore: y = C1*e^-x + C2*x*e^-x + 2x

### Subject: Algebra

Solve the expression: 4(x-2) -3x -6 = 7(x-2) + 12

First use PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction). Then distribute and bring x’s to one side and solve as below: 4x - 8 - 3x - 6 = 7x - 14 + 12 x - 14 = 7x - 2 -12 = 6x x = -2

## Contact tutor

needs and Paul will reply soon.