1. Use separation of variables to find the solution to the differential equation subject to the given initial condition. dy/dx = 5y/x, y = 4 while x = 1
2. Find the solution to the differential equation, subject to the given initial condition.
4(du/dt) = u^2, u(0) = 7

Step-by-step explanation:

Given the differential equation dy/dx = 5y/x subject to the condition y = 4 and x = 1. Using the variable separable method of solving differential equation, we will have;

dy/dx = 5y/x

Separate the variables

dy/5y = dx/x

Integrate both sides of the expression

using the initial condition y = 4 while x = 1

ln4 = 5ln1 + 5C

ln4 = 0+5C

C = ln4/5

Substituting the value of C back into the expression;

Hence the solution to the differential equation is y = 4x⁵

b) Given 4(du/dt) = u²

du/dt = u²/4

du/ u² = dt/4

u⁻²du = 1/4 dt

integrate both sides of the equation

Imputing the initial condition u(0) = 7 i.e when t = 0, u = 7

Hence the solution to the DE is

y/x=18

step-by-step explanation:

0 is its x and y coordinate