Chapter 6: Q. 21 (page 570)

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
$\frac{d y}{d x} = 2 x y$

Short Answer

Expert verified

Ans: The solution of the differential equation $\frac{d y}{d x} = 2 x y$ is $y = A e^{x^{2}}$

Step by step solution

Step 1. Given information.

given,

$\frac{d y}{d x} = 2 x y$

Step 2. Consider the differential equation defined by equation (1) given below and solve it by using antidifferentiation and/or separation of the variable method.

$\frac{d y}{d x} = 2 x y . . . . (1)$

Step 3. Now,

Noe that the differential equation $(1)$ is of the form of $\frac{d y}{d x} = p (x) q (y)$ in which $p (x) = 2 x$ and $q (y) = y$ . So the differentialequation can solved by applying variable separable method. Separate the variables and integrate both the sides

role="math" localid="1649166162207" $\begin{aligned} \int \frac{1}{y} d y = \int 2 x d x \\ \ln | y | = x^{2} + C \\ y = e^{x^{2} + C} \\ = A e^{x^{2}} (e^{c} = A) \end{aligned}$

Hence a solution to the differential equation $\frac{d y}{d x} = 2 x y is y = A e^{x^{2}}$ .

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Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
$\frac{d y}{d x} = 2 x y$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the differential equation defined by equation (1) given below and solve it by using antidifferentiation and/or separation of the variable method.

Step 3. Now,

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Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants. dydx=2xy

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the differential equation defined by equation (1) given below and solve it by using antidifferentiation and/or separation of the variable method.

Step 3. Now,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
$\frac{d y}{d x} = 2 x y$