for each of the following equations, specify its type (order? linear? homogene?) and solve it, specifying on which domain(1)2 = z + x(3) y + 2xy = 0avec y(0) = 1%3D%3D

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Answered: for each of the following equations,…

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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Solve the equations below: x(x - 1) = 30 3x³ + 42x² = -134x 2x³ + 3x²8x = 12 x - 8[3x - (2-x)] = 0 4xy² (3x³y - 5xy) = 0, Let y = 2
Two objects, A and B, are moving along two different straight lines at constant speeds. With reference to a particular coordinate system in which distance is measured in metres, the position of A at time t (in minutes) is (2t − 1, 3t + 3), and the position of B is (5t − 2, 2t + 5). Let d be the distance between A and B at time t. Show that an expression for d 2 in terms of t is given by d 2 = 10t 2 − 10t + 5.
Civil engineers often use the straight-line equation, y = bo+b ₁x, to model the relationship between the shear strength y of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 resulted in a Coefficient of Determination of 0.7589. Given that r 2_ 0.7589, give a practical interpretation of r2, the coefficient of determination for the least squares model. In repeated sampling, approximately 75.89% of all similarly constructed regression lines will accurately predict shear strength. We expect about 75.89% of the observed shear strength values to lie on the least squares line. We expect to predict the shear strength of a triplet test to within about 0.7589 tons of its true value. About 75.89% of the total…
The dual of the equation (y + 1) is

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for each of the following equations, specify its type (order? linear? homogene?) and solve it, specifying on which domain (1) 2 = z +x (3) y+2ry = 0 avec y(0) = 1