Solve the following exact equations: 1) (сos 2y — 3x*y*dx + (сos2y — 2xsin 2y -2x'y)dy %3Dо 2) (2ху- tan y)dx + (x* —xsec? у)dy - 0

Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

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Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

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Q: I am still having troubles trying to effectively solve e^6x(cos7x)dx by integration by parts.

A: Let u = cos7x , dv=e^6xIntegrating by parts:

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

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Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: 4. Find the General and Particular solution of dy -8 sin 4x ; y = 6 when x = 0 dx dy

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Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: Solve 3e* tan y dx+(1-e*)sec² y dy = 0.

A: To solve the given differenrial equation.

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: dy tan tan x = 0 dx coscos x +

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Q: Solve the initial value problem. (tan (2y) - 5)dx+ 2x sec (2y)+ y (2y)+dy=0, y(0) =1

A: Here we have to solve given initial value problem,

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: x3sec2y dy/dx+3x2tan y=cos

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Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 => cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: dy - x X, y(0) = -4 dx Need Help? Watch It

A: using variable separable and then integrate both side...

Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = 0

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Q: 1. Find the general solution (5x*y – sin (x))dx +(2x°y-cos (y))dy = 0

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Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

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Q: S csc“(3y)dy

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: y" + 4y = 2 sin(6x)+ 6x²e¬3z + 5x,

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Q: 3. (x² – xy + y²)dx – xy dy = 0

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Q: 7. 2r tan y dx + sec² y dy = 0

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: Intergrate:

A: To evaluate the integral.

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: Solve the differnetial equation: dy/dx=3/x^2-3x^2+2 with the initial conditions (1,8). show work

A: By using variable separable method we can calculate the given differential equation. See attached…

Q: Solve the initial value problem.

A: To solve the initial value problem.

Q: Solve the initial value problem dx 2x = cos(4t) dt with x(0) = 1. x(t) = sqrt(-1/4sin(4t)+1)

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Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: х2 9 dy + sinx - у %3D0 dx

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Q: find the PS of (16x+5y)dx +(3x+y)dy= 0. if the curve to pass thru the point (1,-3

A: 16x+5ydx+3x+ydy=0 -1equation 1 can be written as

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: solve the Initial Value Problem using Separation of Variables. y' = cos2x, y(0) = π/4

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Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.

Q: dx dy dx dy Use elimination to solve: + = e'; -= *+

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.