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Certain indefinite integrals such as Je dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (inte variables and definite integration to find an explicit solution to the initial value problems in parts a-c, and use Simpson's rule with n= 4 to approximate an answer to part b at x=0.5 to three decimal places. Click the icon to view an example of this process. dy a. Solve the initial value problem with y(0) = 3. Use t as the variable of integration in the explicit solution. y(x) = b. Solve the initial value problemy, with y(0) = 4. Use t as the variable of integration in the explicit solution. y(x) = dy c. Solve the initial value problem =√1+ sinx(1 + y²), with y(0) = 1. Use t as the variable of integration in the explicit solution. y(x) = d. Use Simpson's rule with n= 4 to approximate the solution to part b at x = 0.5 to three decimal places. Click the icon to review Simpson's rule. y(0.5) (Round to three decimal places as needed.)

Certain indefinite integrals such as Je dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (inte variables and definite integration to find an explicit solution to the initial value problems in parts a-c, and use Simpson's rule with n= 4 to approximate an answer to part b at x=0.5 to three decimal places. Click the icon to view an example of this process. dy a. Solve the initial value problem with y(0) = 3. Use t as the variable of integration in the explicit solution. y(x) = b. Solve the initial value problemy, with y(0) = 4. Use t as the variable of integration in the explicit solution. y(x) = dy c. Solve the initial value problem =√1+ sinx(1 + y²), with y(0) = 1. Use t as the variable of integration in the explicit solution. y(x) = d. Use Simpson's rule with n= 4 to approximate the solution to part b at x = 0.5 to three decimal places. Click the icon to review Simpson's rule. y(0.5) (Round to three decimal places as needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Certain indefinite integrals such as Sex dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (integrals with variable upper limit). Use separation of variables and definite integration to find an explicit solution to the initial value problems in parts a - c, and use Simpson's rule with n = 4 to approximate an answer to part b at x = 0.5 to three decimal places. Click the icon to view an example of this process. a. Solve the initial value problem y(x) = b. Solve the initial value problem y(x) = c. Solve the initial value problem dy dx = x², with y(0) = 3. Use t as the variable of integration in the explicit solution. dy 1, with y(0) = 4. Use t as the variable of integration in the explicit solution. dy dx =√1+ sinx (1+y²), with y(0) = 1. Use t as the variable of integration in the explicit solution. y(x) = d. Use Simpson's rule with n = 4 to approximate the solution to part b at x = 0.5 to three decimal places. Click the icon to review Simpson's rule. y(0.5) (Round to three decimal places as needed.) G
Transcribed Image Text:Certain indefinite integrals such as Sex dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (integrals with variable upper limit). Use separation of variables and definite integration to find an explicit solution to the initial value problems in parts a - c, and use Simpson's rule with n = 4 to approximate an answer to part b at x = 0.5 to three decimal places. Click the icon to view an example of this process. a. Solve the initial value problem y(x) = b. Solve the initial value problem y(x) = c. Solve the initial value problem dy dx = x², with y(0) = 3. Use t as the variable of integration in the explicit solution. dy 1, with y(0) = 4. Use t as the variable of integration in the explicit solution. dy dx =√1+ sinx (1+y²), with y(0) = 1. Use t as the variable of integration in the explicit solution. y(x) = d. Use Simpson's rule with n = 4 to approximate the solution to part b at x = 0.5 to three decimal places. Click the icon to review Simpson's rule. y(0.5) (Round to three decimal places as needed.) G
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