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Steps:

1. Use the auxiliary equation on the equation given in the question
2. Solve the resulting equation
3. Identify the appropriate complementary function from the solutions
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a) Create an inequality in x: (x+3)(x-4)<2. Expand and find the critical points, x^2-x-14>0. Find the answers to this inequality using quadratic formula and then test for a value between your two cr...

Let the 2x2 matrix= A. Using the characteristic equation for A (det(A-λI)=0), find the determinant of the matrix (2-λ,1) and (3,-λ). This results in the quadratic λ^2-2λ-3 so λ=3,-1. From the definition o...

We first apply a simple addition to make the inequality 0 on one side. We subtract 10, giving x^2-4x-12<0. Now we factorise the equation in x, intuitively or using the quadratic formula: x=(-b+sqrt(b^2...

(In terms of formatting, we'll use y' to represent dy/dx, exp() to represent the expoential e^(), int() to represent integration with respect to x, and 1ODE to mean First-Order Ordinary Differential Equat...