4. Šolve Člairaut equation y = xy' – 2In(y' +1)

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: y" + 9y' + 7y = e-2t ,t > 0[

A: Using method of Laplace Transform.

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

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Q: 2. Find general solution of the differential equation. y" + y' = tan x

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Q: Solve the differential equation: = 2y- 10 if y = 15 when x = 0. %3D dx

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Q: find general solution of following differential equations: y'tanx=2y-8,y(1/2pie)=0

A: Given differential equationy'tan x = 2y-8⇒ y' = 2ytan x- 8tanx         ∴ y' = dydx⇒ dydx - 2tan x. y…

Q: Show that y = cos xsin x is the solution of the differential equation y'+y tan x cos x

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Q: Find the general solution of the differential equation. y′ = arctan x/ 2

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Q: find solution of order differential equation  dy/dx=cos2(x-y+1)

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Q: Find the particular solution to the differential equation. 4y2 dx = 9x2 dy   when x=4 and y=-3

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Q: ordinate at x = 3. 36. Solve the differential equation (x-2)(x+3)-- (2x+1)3D0 given that y= In6 when…

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Q: 4. Choose a solution to the differential equation y" + 3y' + 2y = sin eª.

A: Here we solve the differential equation using variation of parameter.

Q: dy +y 4)/2=x

A: Consider the following substitution: xy=u   ⇒   xdydx+y=dudx        and        y=ux

Q: solve the differential equations by using integrating factor y'= (y/x) + 2x+1.       when ; y(1)= 3

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Q: Solve Bernoulli differential equation of y' + xy= ry². %3D

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Q: Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Solve the differential eqyations y" – y'+6y =e -2x

A: Differential equation problem.....

Q: Find the general solution of the differential equation y′ = tan3 3x sec 3x

A: Given: y' = tan3(3x)sec(3x) =>dy/dx = tan3(3x)sec(3x) =>dy = tan3(3x)sec(3x) dx

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Solve for homogenous differential equation (x + y)dx + 2xdy = 0

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Q: Find the particular solution to the differential equation. 2y2 dx = 9x2 dy when x = 2, y = -3

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Q: Find the particular solution to the differential equation. 2y2 dx = 3x2 dy when x = 2, y = -1

A: this is variable separable differential equation will separate the variables on both sides and then…

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

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Q: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: 3x + y + z = 0; z(0) = −1

A:

Q: Find the general solution of the differential equation y′ = √(tan x) sec4 x

A: The function is y'=tan xsec4x. To find the general solution, integrate both sides of the equation.…

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION хdy — ydx 4. | = x³ dx y2

A: Given that: xdy-ydxy2=x3dx

Q: Find the general solution of the differential z-y+3 equation y' I-y

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Q: y" + 4xy' +(4x² + 2)y=8e¯x(x+²); _y₁ = è¯ e

A: This is a problem of differential equation.

Q: (f) y' – 2y = 1 + 2x – sin(x)

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Q: 2ydx+x(x² In y-1)dy=0

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Q: Find the differential equation which has y= asinx+bcosx+xcosx

A: Given: y=asinx+bcosx+xcosx                                   ..1 for finding differential equation…

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos ex y(x) =

A: Given differential equation is y''+3y'+2y=cos ex The auxiliary equation is…

Q: Find the differential equation having as solution of y = x sin(xtc) .

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Q: Solve the differential equation by variation of parameters. y" + y = sin(x) y(x) = %3!

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Q: The Integrating Factor of the differential equation dy dr y = 14x? is x-14 25 e5z

A: The given differential equation is,  dydx-5xy=14x2To find its integrating factor.

Q: y' - 2x = -e-t; y(0) = 2

A: y' - 2y = - e-t, y(0) = 2 Thia is a linear differential equation of first order  Integrating factor…

Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

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Q: What differential equation has y = x² cos y - 4x + C as a solution?

A: We have to find

Q: Solve for first odrer differential equation    (x^2+cosy)dy+(3x^2+2xy)dx=0 where; x=0 , y=π/2

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Q: Find general solutions of the differential equation    (x+y)y'=1

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Q: 2) Obtain the differential equation of parabolas with vitex and focus on the x-axis

A: To find: the differential equation of parabolas on the x- axis.

Q: solve for Differential Equation y(x2+2)dx - (x2-x)dy = 0 when x= sqrt 3 and  y= 1/3

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Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: 2. Solve (implicitly) the Exact Differential Equation 2x + y° sec²x)dx + (1 + 3y²tan x)dy = 0.

A: Given differential equation is: 2x+y3sec2xdx+1+3y2tanxdx=0 To solve the given differential equation.

Q: Q3: if y'-f(y/x) where v-y/x Find a solution to the differential equation 2xyy'-y2+x2 =0 ?

A: Given

Q: 5. Find the solution of the differential equation using Variation of Parameters. y"' – 3y" + 3y' =

A: We will use the method of variation of parameters to solve this question. First, we find the three…

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.