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Each of the following is an exact differential. Practice making the test to show this. Solve it and find the specific solution by applying the given condition. For each question supply the following: The functions (y,x). Pay careful attention to the constant functions with the answer boxes. For example y2 +3-x-y should go in the first answer box and x+3x-y in the second for part a. Don't forget to insert a space or multiplication symbols between x & y to avoid answer entry errors. The final answer box is for the problem's solution with the condition applied. For part a. your answer should be x²+3x-y+y²=1. = (0)3y) dx = o with y + 32) + بری (2y+3x) .2 30 + تر = (x) (r) - 2+1 x x (x) = (۲) . 1 = 3 + - د - (x) = قير * h(y) 2 = (0)d = 0 with y (2+1 + راه اه + رشد) .۵ | + (x) + hy) = الي + 2 + 3 = (x) و 2 = (0)x = o with y ) + ك ( - ) » (ان + (x) (x) - (x) = x = y = =2 + (۷) ✓

Each of the following is an exact differential. Practice making the test to show this. Solve it and find the specific solution by applying the given condition. For each question supply the following: The functions (y,x). Pay careful attention to the constant functions with the answer boxes. For example y2 +3-x-y should go in the first answer box and x+3x-y in the second for part a. Don't forget to insert a space or multiplication symbols between x & y to avoid answer entry errors. The final answer box is for the problem's solution with the condition applied. For part a. your answer should be x²+3x-y+y²=1. = (0)3y) dx = o with y + 32) + بری (2y+3x) .2 30 + تر = (x) (r) - 2+1 x x (x) = (۲) . 1 = 3 + - د - (x) = قير * h(y) 2 = (0)d = 0 with y (2+1 + راه اه + رشد) .۵ | + (x) + hy) = الي + 2 + 3 = (x) و 2 = (0)x = o with y ) + ك ( - ) » (ان + (x) (x) - (x) = x = y = =2 + (۷) ✓

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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Each of the following is an exact differential. Practice making the test to show this. Solve it and find the specific solution by applying the given condition. For each question supply the following: - The functions \( u(x,y) = x \). Pay careful attention to the constant functions with the answer boxes. For example: \( x^2 + 3xy \) should go in the first answer box and \( x^2 + 3 \times xy \) in the second for part a. Don’t forget to insert a space or multiplication symbols between x & y to avoid answer entry errors. The final answer box is for the problem’s solution with the condition applied. For part a, your answer should be \( x^2 + 3 \times xy + y^2 = 1 \). a. \((2x+3y)dy + (3x^2+3y)dx = 0 \) with \( y(0) = 1 \) - \( u(x,y) = \) - Box 1: \( x^2 + 3xy \) ✗ - Box 2: \( y^2 + 3xy \) ✗ - Box 3: \( x^3 + y^2 + 3xy \) = 1 ✓ b. \((3x^2 + 2e^y)dy + (2y + 2x^3)dx = 0 \) with \( y(0) = 2 \) - \( u(x,y) = \) - Box 1: (empty) - Box 2: (empty) - Box 3: \( x^3y + 2x + e^y = 2 \) ✓ c. \((xe^{y} - 1)dy + (e^{x})dx = 0 \) with \( y(0) = 2 \) - \( u(x,y) = \) - Box 1: (empty) - Box 2: (empty) - Box 3: \( xe^y - y = 2 \) ✓
Transcribed Image Text:Each of the following is an exact differential. Practice making the test to show this. Solve it and find the specific solution by applying the given condition. For each question supply the following: - The functions \( u(x,y) = x \). Pay careful attention to the constant functions with the answer boxes. For example: \( x^2 + 3xy \) should go in the first answer box and \( x^2 + 3 \times xy \) in the second for part a. Don’t forget to insert a space or multiplication symbols between x & y to avoid answer entry errors. The final answer box is for the problem’s solution with the condition applied. For part a, your answer should be \( x^2 + 3 \times xy + y^2 = 1 \). a. \((2x+3y)dy + (3x^2+3y)dx = 0 \) with \( y(0) = 1 \) - \( u(x,y) = \) - Box 1: \( x^2 + 3xy \) ✗ - Box 2: \( y^2 + 3xy \) ✗ - Box 3: \( x^3 + y^2 + 3xy \) = 1 ✓ b. \((3x^2 + 2e^y)dy + (2y + 2x^3)dx = 0 \) with \( y(0) = 2 \) - \( u(x,y) = \) - Box 1: (empty) - Box 2: (empty) - Box 3: \( x^3y + 2x + e^y = 2 \) ✓ c. \((xe^{y} - 1)dy + (e^{x})dx = 0 \) with \( y(0) = 2 \) - \( u(x,y) = \) - Box 1: (empty) - Box 2: (empty) - Box 3: \( xe^y - y = 2 \) ✓
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