Determine the a interval for which the solution is defined, Solve: x dy + y dx =

Question

Determine the a interval for which the solution is defined, Solve: x dy + y dx = y dy Does the equation x2 dx + y dy = 3 make sense? Explain. Explain why the general first-order equation M(x,y) dx + N(x,y) dy = 0 cannot be solved by separation of variable. Give an example of such a equation. Solve y' =f(y/x) by making the substitution y = vx and showing the the differential equation in the variables v and x can be solved by separation of a variables. The first-order linear differential equation A particularly important type of first-order equation is the linear equation a(x)dy/dx + b(x)y = c(x) If a(x) is not zero in some interval, we may divide by a(x) to obtain dy/dx + P(x)y = Q(x)

Explanation / Answer

it is actually saying about equation which are homogeneous in nature of form y/x... they can be solved by making y/x = m change the differential to dy/dx = m + x dm/dx : and it becomes variaable separable form

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