- It is known that y1 (x) = x and y2(x) = x are solutions of the differential equation xy" - 2xy + 2y = 0. %3D (a) Verify that y3(x) = 2x + x is also a solution of the differential equation. (b) Use the Wronskian to determine whether y1, y2 and y3 are linearly dependent on the interval (0, 00).

Q: Consider the differential equation x²y" 4xy' + 6y=0; x², x³, (0, 0). Verify that the given functions…

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Q: Check that the indicated function is an explicit or implicit solution of the given differential…

A: Consider the differential equation dydx=xy+3x−y−3xy−2x+4y−8 Hence,  dydx=xy+3x−y−3xy−2x+4y−8…

Q: The differential equation y" + p(x)y' + q(x)y = 0 is known as a homogeneous second-order linear…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: We have to find the value of y2(x) To find this we using formula (5)

Q: Match the differential equation y′ − 2xy = x with its solution as attached.

A: Given: y'-2xy=x for solving this we will use variable separable method we know that y'=dydx

Q: y = 1/(x² + c) is a one-parameter family of solutions of the first-order DE y' + 2xy² = 0. Find a…

A: The objective of the question is to find the solution of the first-order initial value problem…