MATH 1B Lecture Notes - Lecture 14: Slope Field, Product Rule
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Math 1b: calculus - lecture 14: solving differential equations. A: we have (dy/dx) = 5y. (1/y) (dy/dx) = 5. (1/y) (dy/dx) dx = 5 dx. ln(|y|) = 5x + c, where c is a constant. F(u) (du/dx) dx = f(u) du. If u = sin(x), then du = cos(x) dx. Look up the slope field for the homework problem from last time. (stated above). We may state differential equations of the form. (dy/dx) = f(x) g(y) in this way. A: we have (dy/dx) - y = exy. (dy/dx) = y + e (dy/dx) = y(e (1/y) (dy/dx) = e x + 1. (1/y) (dy/dx) dx = (e ln (y) = e x + 1). xy. x + 1) dx. x + x + c, where c is a constant. You can continue to simplify from here, but note that the equation was changed into the form (dy/dx) = f(x) g(y), where f(x) = ex + 1 and g(y) = y.
