Question

solve x=y+z log p where p=dy/dx

Answer 1

here your answer........

Answer 2

Concept

A variable-exponent equation is referred to as an exponential equation. The term "logarithmic equation" is used to describe an equation that uses the logarithm of an expression comprising a variable. Finding the value of the unknown variable is the goal of solving a logarithmic equation.

Given

x = y ₊ z log p, where p = dy/dx

Find

solve the above equation and get the values.

Solution
given,

x = y ₊ z log p .....eq(1), where p = dy/dx

1/p = 1 ₊ z/p dp/dy

1/p ₋ 1 = z/p dp/dy

1 ₋ p/p = z/p dp/dy

∫ dy = ∫ z/1₋p dp

y = ₋z log (1₋p) ₊ c

y = c ₋ z log (1₋p) .......eq(2)

x = y ₊ z log p

x = c ₋ z log (1₋p) ₊ z log p .....eq(3)

therefore solution is given equation  by 2 and 3 both.

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