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In Problems 1-7, convert the given initial value problem into an initial value problem for a system in normal form.
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Fundamentals of Differential Equations and Boundary Value Problems
- Let F = V where (x, y, z) x2 1 + sin² 2 +z2 and let A be the line integral of F along the curve x = tcost, y = t sint, z=t, starting on the plane z = 6.14 and ending on the plane z = 4.30. Then sin(3A) is -0.598 -0.649 0.767 0.278 0.502 0.010 -0.548 0.960arrow_forwardLet C be the intersection of the cylinder x² + y² = 2.95 with the plane z = 1.13x, with the clockwise orientation, as viewed from above. Then the value of cos (₤23 COS 2 y dx xdy+3 z dzis 3 z dz) is 0.131 -0.108 -0.891 -0.663 -0.428 0.561 -0.332 -0.387arrow_forward2 x² + 47 The partial fraction decomposition of f(x) g(x) can be written in the form of + x3 + 4x2 2 C I where f(x) = g(x) h(x) = h(x) + x +4arrow_forward
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- Please solve handwritten, without use of AIarrow_forwardUse Euler's method with step size h = 0.1 to approximate the solution to the initial value problem y' = x - y², y(3) = 0, at the points x = 3.1, 3.2, 3.3, 3.4, and 3.5.arrow_forward2. Let f(x) = 2x² + 6. Find and completely simplify the rate of change on the interval [3,3+h]. (5 points)arrow_forward
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