1. y" + 4y' + 4y = e-2x %3D x2

Q: General solution of 2xydx+y^2dy=0

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Q: Differentiate. x4 y: 3 — х3 y' У -

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Q: '= -x+y - 8

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Q: 9. f²-2x(3x - 1) dx

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Q: Differentiate. y = In (6x? - 5x + 3) y' =O

A: Given: y=ln6x2-5x+3 We know that ddxlnx=1x…

Q: 1. f4x-³ dx -3

A: Find the integral

Q: y = 5t2 - 2t + 4 -'(t) =

A: The given function is y=t25t2-2t+4. We have to find the derivative of the given function. The…

Q: 4. 16x – 2x2 – 23 dx -

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Q: ду Find ду and when dz (a) y = 6 + 3x + 16z + 4x2 + 2z2 (b) y = 14x2 (c) y = 9 + 4xz - 3x2 %3D

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Q: 4= Find y 13x+(2x3-x'

A: To find the derivatives

Q: 3 3 + x 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: А сurve bas equation y%3 (x+3}x* -3х+6). Explain wһу у%3(х+3Xx*-3х+6) is always positive for x>-3.

A: The solution is :

Q: Find the solution. dy x+5y=2x?y+ dx

A: We have to solve the given differential equation.

Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: find dp/ dq. sin q + cos q = cos q

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Q: Зу" +y=0.

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Q: 3 = 4- 2y + - dx

A: The differential equation is,   The figure below represents the vector field of the differential…

Q: * Salne the equalion:- (2x-44 +5)y'=n -2y+3

A: This homogeneous differential equation is solve by substitution and then by separation of variables…

Q: 5. y" - 4y = 0 6. y" - 64y = 0

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Q: x² + 8x + 5 x³ + 8x / dx

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Q: exapy %3D 4-x2

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Q: What is the independent variable, order and degree of 5y′′−(y′)4=y^3sinx

A: Topic :- Differential equation

Q: Find the solution of the D.E whose solution is given as y=2(x^2−1)+ce−x^2

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Q: y' = 2x + 14

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Q: Differentiate y = xe у'3

A: Apply product rule. (uv)'=u'v+uv'

Q: 6/T-9x dx

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