MATH 2Z03 Quiz: tutorial3.pdf
3 Dec 2014
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De nition 3. 1 a rst order di erential equation of the form is said to be a linear equation in the dependent variable y. a1(x) dy dx. If g(x) = 0, the linear equation is said to be homogenous; otherwise, it is called nonhomogeneous. Any such linear rst order o. d. e. can be re-arranged to give the following standard form: dy dx. The homogenous di erential equation (3. 2) is also separable. Example 3. 1. 1 solve the following di erential equation dy dx. + 2xy = 0, y(0) = 1 (3. 1) (3. 2) Solution: this is rst order linear homogenous di erential equation, here p (x) = 2x. 3. 1. 2 solution to inhomogeneous des using integrating factors. To solve a rst-order linear in homogenous di erential equation (3. 1), you can use an inte- grating factor u(x) which converts the left side of (3. 1) into the derivative of the product u(x)y. That is, you need a factor u(x) such that u(x) u(x) dy dx dy dx.
