MATH150T2

# MATH150T2 - MATH 150 Separable Equations Cheung Man Wai...

This preview shows pages 1–3. Sign up to view the full content.

MATH 150 Separable Equations Cheung Man Wai Tutorial 2 An equation is said to be separable if it can be written in the form M ( x ) dx + N ( y ) dy = 0 . Moreover, if we require the initial condition, namely y ( x 0 ) = y 0 , then we can solve it as x x 0 M ( x ) dx + y y 0 N ( y ) dy = 0 . The crucial step of this method is to rewrite the equation as the form (1) and perform integration thereafter. Now we turn to some examples. Example 1: dy dt = ry , where r is a constant. This eqation is usually called the exponential equation. dy dt = ry dy y = rdt ln | y | = rt + C y = De rt , where C, D are constants. Example 2: Solve y = 1 + y 2 with y (0) = 1. By separating valuables, we have y 1 dy 1 + y 2 = x 0 dx tan - 1 y | y 1 = x | x 0 tan - 1 y - π 4 = x y = tan( x + π 4 ) . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Note that tan is not defined at π 2 + 2 , for n is any integer. And as we have initial value for x = 0, we want - π 2 < x + π 4 < π 2 . Therefore, the solution is y = tan( x + π 4 ) for x ( - 3 π 4 , π 4 ) . Example 3: Solve y = 2 x/ ( y + x 2 y ) with y (0) = - 2 . We first represent the equation in the form dy dx = 2 x y (1 + x 2 ) and regard dy/dx
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern