3. Show that the function f(x, y) = xy3 - 2x2 y2 is homogeneous. (4 pts.) dy 4. Use an appropriate substitution to solve the differential equation 2y= -7x²y³ dx (8 pts.)

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Q: X = y + % y = 0.000396707 – 0.24576 x2 22 = 0.00029753 - 0.12288 x²

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Q: Find the differential of the function. y = x² - 9x + 2 dy = Evaluate it at the given values of x and…

A: Step 1:To find the differential of the function y=x2−9x+2, we'll use the definition of the…

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A: Given the differential equation is y" - y' - 2y = 0. Here the auxiliary equation is m2 - m - 2 = 0

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Q: ind the general solution of the differential equation given below using the Parameter Variation…

A: 3x2y''+11xy'-3y =10x-10 to find C.F 3x2y''+11xy'-3y=0 Put ez=x  , z =logx 3D(D-1) +11D-3=0…

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A: Multiple questions:Since you have asked multiple questions, we will solve the first question for…

Q: 3. Find the complete solution of the differential equation (4x + xy2) – (y – x?y)y' = 0 using…

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Q: B. ty" – (t+ 1)y' + y = t?

A: Answer is mentioned below

Q: (2.) Find the general solution to y' + 2ty = 5t.

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Q: Solve the following differential equations: 2x a) + 2y = xy², y(0)=1 dy 3 b) x - y = 4x³y-¹cos(x)

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Q: I (2x3+ y) dx – x dy = 0 2. y dx - (x + 6 y2) dy = 0 3. (x+y) dx + tan(x) dy = 0 4. 6Xy dx + (4y+ 9…

A: As per our guidelines, I can answer only one question. Since you have asked for multiple questions,…