Question

Given the following ordinary differential equation, its solution is dy/dx = 3x/4y

a) y = ✓(3x²)/2
b) y = 4*✓(1+x²)/3
c) y = 3*✓(1+x²)/4
d) y = 3*✓(1-x²)/4

Answer 1

The solution to the differential equation dy/dx = 3x/4y can be found by separating variables and integrating, resulting in the general solution y = √[(3/4)x2 + C]. The closest matching solution provided is a) y = √(3x²)/2 when C is set to zero.

Step-by-step explanation:

The student has asked how to solve the ordinary differential equation dy/dx = 3x/4y. To find the solution to this equation, we need to integrate both sides. Separating the variables y and x, we can rewrite the equation as 4y dy = 3x dx. After integrating both sides, we obtain y2 = (3/4)x2 + C, where C is the integration constant. Solving for y, we have y = √[(3/4)x2 + C]. We match this general solution to the given options and notice that none of the provided options has an additional constant C; hence we set C to zero for simplicity and to align with the provided answers. The closest matching option with C=0 is option a) y = √(3x²)/2.