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ENGINEERING MATHEMATICS - EXAMPLE 8.3 : Solve the first order differential equation : (Z + 1)(dy/dx) = xy in term of ln |y| = f(x). Z = (x)(x).
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Answer Posted / kangchuentat
ENGINEERING MATHEMATICS - ANSWER 8.3 : Rearranging the equation (1/y)(dy) = [ x / (Z+1) ] (dx). Use the additional equation u = Z + 1, du = 2x dx, 0.5 du = x dx. Then the equation becomes (1/y)(dy) = (0.5)(1/u) du. Integrating both sides of the equation gives ln |y| = (0.5) ln |Z+1| + c where Z = square of x. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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