Solve using selaration of variables: xy^3 dx + ex^2 dy = 0.

Q: Solve for the particular solution: (D² - 2D + 6)y = 4e-2x O yp = (-1/2) e^(-2x) O yp = -2xe^(-2x) O…

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Q: Solve using Undetermined Coefficients 7.D¹y = 5x

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Q: Solve using 2 techniques: (x^2+6y^2)dx−4xydy=0; x=6,y=9

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Q: Differentiate y = 3e2x/(1 + x2.)

A: y=3e2x1+x2

Q: Reduce to lowest terms: x'+3x++2x+6 x+3

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Q: Solvedy =dy +4y=2= dx

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Q: .2 Solve y²dx + (x Vy? – x² – xy) dy = 0

A: To solve the following differential equation

Q: 1. Solve the nonlinear equation x - 5 y? dy dx

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Q: y = In( sech2x)

A: The objective of the question is to find the derivative of the function y = ln(sech^2(x)).

Q: xdy − ydx = x^2dy, Solve for D

A: We can solve the DE as below

Q: Solve yuyx - Ux=4/x

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Q: Solve the equation (x^4 + 2y)dx - xdy = 0

A: I am attaching image so that you understand each and every step.

Q: 4. Let u₁ (1,0, 0, 0), u2 = (1,1,0,0), u3 = (1,1,1,0), u4 = (1,1, 1, 1) be the vectors in R4.…

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Q: Linearize the non-linear equation: 1. y=c+ax^n

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Q: Solve (D^2+2D-1)y=0

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Q: Solve the differeial equation: dy/dx=3x^2y^2

A: The given differential equation is dydx=3x2y2.

Q: Solve (2x^2y +y)dx+xdy =0

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Q: [x' 9 -x dx

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Q: Simplify (5x'yz)

A: Given, (5x3y-2z4)3

Q: y(6y^2-x-1)dx + 2xdy =0

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Q: 6/T-9x dx

A: Here we have to integrate        ∫[(6√x - 9x)/x2] dx