In Exercises 3–6, find the general solution of the differential equation and check the result by

step 1 Okay, so given D .YDX is equal to X to the three halves, to integrate that, we need to find the

In Exercises 3–6, find the general solution of the...

Key Concepts

Verification by Differentiation

Verification by differentiation involves checking the obtained solution by differentiating it. This step confirms that the differentiated form matches the original differential equation, ensuring the correctness of the solution.

Indefinite Integration and Antiderivatives

Indefinite integration is the process of finding the antiderivative of a function, which is fundamental in solving differential equations. The antiderivative is a function whose derivative gives the original function, and this step is essential for obtaining the general solution.

Constant of Integration

When performing indefinite integration, a constant of integration is added to account for the fact that differentiation of a constant yields zero. This constant represents the family of all possible solutions to the differential equation.

Ordinary Differential Equations

An ordinary differential equation (ODE) involves functions of a single variable and their derivatives. ODEs model a variety of phenomena, and solving an ODE involves finding a function that satisfies the relationship between its derivatives and the function itself.

Separation of Variables

Separation of variables is a method used for solving differential equations that can be rearranged so that all terms involving one variable are on one side of the equation and all terms involving the other variable are on the opposite side. This technique simplifies the equation into integrable parts.

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