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How do you find the general solution of a second order differential equation?

Steps: Use the auxiliary equation on the equation given in the question Solve the resulting equation Identify the appropriate complementary function from the solutions Determine an appropriate particular int...
OD
3687 Views

Find the values of x where x+3>2/(x-4), what about x+3>2/mod(x-4)?

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 criti...
BH
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FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)

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 of t...
BM
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Find values of x which satisfy the inequality: x^2-4x-2<10

We first apply a simple addition to make the inequality 0 on one side. We subtract 10, giving x^2-4x-12&lt;0. Now we factorise the equation in x, intuitively or using the quadratic formula: x=(-b+sqrt(b^2-4a...
RK
4986 Views

I'm struggling with an FP2 First-Order Differential Equations Question (Edexcel June 2009 Q3) and the topic in general!

(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 Equation...
LB
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