Sketch the graph of the inhomogeneous term and find the solution to the initial value problem: + dy=sent-u(t)sen(t-2n). y(0) 0, y'0)- 0.

Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: Find the GS of 2 (x - α)² = where a is an arbitrary constant and you may want to consider "pilot" y₁…

A: As per the question we are given the following nonlinear first order differential equation…

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: Find the particular solution to the equation y'' – 8y' + 16y = 4e# ln t Y>(t) = %3D

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Q: a function y = f(x) be implicitly given by the equation y²-x²y³ - cos (πy) = xª. The point (-1,1).

A: Topic:- application of derivatives

Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: dy dx 3x² + 4x + 2 2(x - 1) y(0) = -1. . Check if it has a unique solution in some interval about x…

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Q: Solve dy dy dr? + y = 2sin(3r) dr using the method of undetermined coefficient.

A: We will solve by undetermined coefficient method

Q: Solve the equation y" + 36y= exp(2x) where y(0) = y'(0) = 0.

A: Given: y"+36y=exp(2x); y0=y'0=0To find: yx

Q: (b) Solve: (x*D² - 2XYDD' - 3y'D? +xD-3yD')z = x'ycos(Inx').

A: