# Differential Equation : Find General Solution

Not what you're looking for?

Please see the attached file for the fully formatted problem.

Find a general solution on (-pi/2, pi/2) to y'' + y = tan x given that S secx dx = ln |sec x + tan x|.

##### Purchase this Solution

##### Solution Summary

A general solution is found to a differential equation. The solution is detailed and well-presented.

##### Solution Preview

Please see the attached file for the complete solution.

(i) This equation is in the standard form: y'' + y = tanx

(ii) The associated homogenous equation is y'' + y = 0

The characteristic equation is: λ2 + 1 = 0

λ1 = i and λ2 = -i

yh = c1 cos x + c2 sin x

y1 = cos x, y2 = sin x, g(x) = tanx

y1' = -sin x, y2' = cos x

(iii)

(iv)

(v)

(vi) yp = u1y1 + u2y2 = cos x(sin x - ln (secx + tanx)) - sin x cos x

= -cos x ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability