Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b. (e"cos(x))y' x4 + 6x²y³ C. y' = y + vx3 x + x2 cos() cOS

Q: 1. 2. (√ex + (ex)³) dx /22sinx cos x dx

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Q: x*cos(y/x)*dy/dx = y*cos(y/x)-x   find solution of that differantial equation.

A: Let us consider the differential equation of the form dydx=fyx  then to solve the differential…

Q: 2. f cos³ (20x)dx

A: Given :

Q: If y = cos¹ (v₁²), X = find dz? 1 Vu² +1 2= ln (2x-3y)

A: Consider the given equations, y=cos-1vu2x=1vu2+1z=ln2x-3y here we need to find the value of dz.…

Q: 6. Find dy dx of cos y - 2xy + 3x = 2x sin x

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Q: .v" + y = cos x ; when x = 0, y = 0, y' = 1

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Q: S(;+ sin(x) – Vx²) dx

A:

Q: a Jx'cos(x')dr= a d. 1 sin(*) +C sin +C e -sin sin(x') +C sin(x 3 3 +C 3

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Q: Differentiate the equation below with respect to x: 3e" + x' = 4x- 5y

A: Here we have given a equation : 3e2y+x3=4x-5y2. Now differentiating both sides w.r.t  'x' we get :…

Q: dx (x – 2)Vx² – 4x +3 dx sin-1xV1- x2 L. cos(sec xVx2 – 1 -x) dx 2/V3

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Q: 37/2 8 cos x dx T/2

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Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: Solve dy dx + y tan x = -y³x sec²(x)

A:

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

A: Given: 1.xy+y2=1 , 2. x2y-xy2+x2+y2=0 3. x2-xy+y2=3 4. x3y+xy2=3 and x=1

Q: x° + x2 + 1 (c) dx. x3 – x2 +2x - 2 arctan x (d) x2

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Q: ル。 dz = 2. For z = -5x* - 6y and a Point P ER' we have dz 23 dy Determine the value of

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: dy d. x = y + y³cosx dx

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Q: y " +2y' - 8y = x? + cos x

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Q: sin If y = show that (1- x²) 1-x -1 x. d'y -3x dy drソミ0 dx? ーy=

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Q: Use the method of undetermined coefficients to solve y" – 2y' + y = 5 cos(2x) + 10 sin(2x)

A: Solve the differential equation y"-2y'+y=5cos2x+10sin2x using the undetermined coefficients .

Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

A:

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: Q1) Find the first derivative of the following equations: y = x'V

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Q: 1- 2- If x=y√√1-y², find Find y' for y=cos(sin²x) dy dx

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Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.