show that the following diffrential can be transformed into equations with separ
ID: 1942742 • Letter: S
Question
show that the following diffrential can be transformed into equations with separable variables and then solve it:use y = z(x^3/4)
dy/dx = (2+3x(y^2) ) / (4(x^2) y)
Explanation / Answer
use y = z(x^3/4) dy/dx = (2+3x(y^2) ) / (4(x^2) y) y = z(x^3/4) => dy = dz*(x^3/4) + 3x^2 *z/4 dx => dy/dx = (x^3/4)*dz/dx + 3x^2 *z/4 => (x^3/4)*dz/dx + 3x^2 *z/4 = (2+3x(y^2) ) / (4(x^2) y) => (x^3/4)*dz/dx + 3x^2 *z/4 = 2/(z*x^5) + 3zx^2/4 => dz/dx = 8/zx^8 => zdz = (8/x^8)dx ( Hence variables are separated) on integrating both sides, z^2/2 = (-8/7)x^(-7) + C where C is constant or (4y/x^3)^2/2 = (-8/7)x^(-7) + C
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