Math, asked by shraddhadhangar2000, 1 month ago

The solution of simultaneous differential equations dx/a=dy/a=dz. is

Answers

Answered by Afreenakbar

Answer:

The given differential equations are:

$\frac{dx}{a} = \frac{ dy}{a} = dz$

By seeing the following expressions as ratios and equating them to a fixed amount, which we'll name k, we may solve these equations.

So,

$\frac{dx}{a} = \frac{ dy}{a} = dz$

Our first equation is given by dx = k × da.

By integrating both sides, we arrive at the equation x = ka + C₁, where C₁ is the integration constant.

Similarly, the second equation gives us y = ka + C₂, where C₂ is still another integration constant.

The third equation gives us z = ka + C₃, where C₃ is still another integration constant.

Therefore, the simultaneous differential equations have the following solution:

x = ka + C₁

y = ka + C₂

z = ka + C₃

Here, k, C₁, C₂, and C₃ are arbitrary constants, and a is a parameter in the given equations. The specific values of the constants and parameter would depend on the initial conditions or any additional information provided.