Chapter 2: Q-6E (page 46)

In problem $1 - 6$ , determine whether the given differential equation is separable $s^{2} + \frac{d s}{d t} = \frac{s + 1}{s t}$ .

Short Answer

Expert verified

The given differential equation is not separable.

Step by step solution

Concept of Separable Differential Equation

A first-order ordinary differential equation $\frac{d y}{d x} = f (x, y)$ is referred to as separable if the function in the right-hand side of the equation is expressed as a product of two functions $g (x)$ that is a function of $x$ alone and $h (y)$ that is a function of $y$ alone.

Mathematically, the equation $\frac{d y}{d x} = f (x, y)$ is separable when role="math" localid="1654781548639" $f (x, y) = g (x) + h (y)$ .

Subtracting s2 from both side in the given equation.

Given Equation $s^{2} + \frac{d s}{d t} = \frac{s + 1}{s t} . . . . . . . . . . (1)$

Subtracting from both side in the equation

$\frac{d s}{d t} = \frac{s + 1}{s t} - s^{2}$

Simplifying the above equation

$\frac{d s}{d t} = \frac{s + 1 - s^{2} (s t)}{s t} \frac{d s}{d t} = \frac{s + 1 - s^{3} t}{s t}$

We cannot separate the above expression about terms.

Therefore, the given differential equation is not separable.

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In problem $1 - 6$ , determine whether the given differential equation is separable $s^{2} + \frac{d s}{d t} = \frac{s + 1}{s t}$ .

Short Answer

Step by step solution

Concept of Separable Differential Equation

Subtracting s2 from both side in the given equation.

Simplifying the above equation

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In problem 1-6 , determine whether the given differential equation is separable s2+dsdt=s+1st.

Short Answer

Step by step solution

Concept of Separable Differential Equation

Subtracting s2 from both side in the given equation.

Simplifying the above equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Logic and Functions

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In problem $1 - 6$ , determine whether the given differential equation is separable $s^{2} + \frac{d s}{d t} = \frac{s + 1}{s t}$ .