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Unformatted text preview: Chapter 2. First Order Diﬀerential Equations §2.2 Separable Variables Def: A ﬁrst order diﬀerential equation of the form dy = g (x)h(y ) dx is said to be a separable DE. To solve a separable DE, separate the variables into 1 dy = g (x)dx h(y ) then integrate 1 dy = h(y ) g (x)dx. EX: Solve the following DEs. (1)
dy dx = −x. y = e3x+2y = ky = 5y, y (0) = 100. y (0) = 0. (2) (1 + x)dy − ydx = 0 (3) (4) (5)
dy dx dy dt dy dt dy (6) (e2y − y ) cos x dx = ey sin 2x, (7) dy dx = y2 − 4 1 ...
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