4. Solve the following differential equation over the interval from a = 0 to x = 1 with a step size of 0.25. dy (3) dx Use the following methods and determine the error for each numerical method: (a) Analytically. (b) Euler's method (c) Predictor-corrector method (d) 4th order Runge-Kutta method = (1+2x)√y y(x = 0) = 1

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.