Pr. #2) Solve for y' = by logarithmic differentiation. e sinh(3x + 1) y = (2x + 1)4 5x –1

Q: The solution of the differential equation tan xdx + tan ydy = 0 is

A: Using variable separable method.

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

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Q: 10) 4xy dx - (6x² +y) dy so

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Q: [3 – e -kl – cos x + log(x²)]dx = 0

A: Given,∫a5 3-e-x-cos x+log x2 dx

Q: 1. Xy" + (y)2 - 2xy' = Q

A: We will find solution of given differential equation as shown below

Q: (x+2)? dy 2y dx x -4 x² -4

A: dydx+2yx2-4=x+22x2-4⇒dydx+2yx2-4=x+2x-2⇒y=∫x+2x-2dxx+2x-2x-2

Q: Solve the differential equation: y = 3x +log P.

A: Given equation is y=3x+log P Let us consider P as a constant and then dydx=ddx(3x + log…

Q: i) Solve the differential equation dx +tan x tan y = cos x secy.

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Q: Solve the differential equation (2xy - tan⁡ y) dx + (x^2-x sec^2 y) dy = 0.

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Q: This differential equation is linear. What is the Q(x)? * Cosx dy t (y- cosx )dn = 0

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Q: (1+x*)dy + x(1+ 4y²)dx =0

A: topic- differential equations

Q: Еxample 3: Solve the differential equation xy + 0. dx

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Q: x'+z=et; x(0) = 1

A: Take z as constant

Q: Use exponential shift to find the general solution of the differential equation. (D+1)°y = 0

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Q: 2. Solve the differential equation dy sin x dx 2 y-cot x

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Q: 4. y = x cos(In x) x²y" - xy + 2y = 0

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Q: Find the logistic differential equation dy ky 1-Y dx L

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Q: 1) y"+ y – 2y = e" + 4 sin x + x² – x solve this differential equation from derivative operator.

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Q: Find complementary function of the differential equation  (D2 + 52)y = sin3x

A: The differential equation is D2+52y=sin3x.

Q: The function y(x) is given implicitly by the equation y3−3xy+x3=3. Find its differential at the…

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Q: dy (sec x) dx eуtsin x

A: Given : The differential equation sec xdydx = ey + sin x

Q: Question 7 Solve for the differential ofy when y=sinx, x=-, and dx=- 3 2 A 4 B 元 4.

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Q: dy Solve the differential equation for y if (1+9x²) 1 %3D dx

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Q: Solve the differential equation  xdy-{y+xy3(1+logx)}dx=0

A: Given differential equation is : xdy-y+xy31+logxdx=0 To solve the given differential equation .

Q: Task 2 Verify that the function y(x) = sin(x³) is a solution of the %3D second-order differential…

A: Given  Second order differential equation: y'' - 2/x y' +9x4y=0 To prove : y = sin (x3) is solution…

Q: dy =ky L) dx

A: We will find the logistic differential equation  Where L carring Capacity

Q: Find the differential equation corresponding to y=a cos(logx) +b sin (logx) where a and b are…

A: For a given solution having N constants , we have to differentiate the given solution for N times to…

Q: Solve the differential equation. y" +y = tan x

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Q: Solve the differential equation: (2xy-sinx)dx+(x² - cosy)dy=0.

A: The given differential equation is  (2xy-sinx)dx+(x2-cosy)dy=0 It is of the form , Mdx+Ndy=0 . This…

Q: Solve the differential equation y' =a'y subject to the condition that y = e when x = 0. Preview

A: Y(x)=?

Q: B: Solve the differential equation: (1+x)dy + ydx = tan-1x dx

A: To solve the given differential equation: (1+x2)dy+y dx=tan-1x dx

Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: Find the differential equation corresponding to y=a cos (logx) +b sin(log x)

A: Chain rule of differentiation: [f(g(x))]'=f'(g(x))g'(x) Formulae used: ddxcos x=-sin xddxsin x=cos…

Q: у" + 16у — 0; Уi — сos 4x

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Q: Example 11 : Find the equation of the curve satisfying the differential eguatio- dy (1+x?)+2xy= 4x²…

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Q: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

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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: メ+y= Xex sin 2x t.

A: Given:   y''+y=xex sin2x

Q: dy B)Solve differential equation dx -(sinx+cosy) y²-x siny

A: Exact differential equation

Q: Solve for the differential equation: dy/dx - ytan x = cos x

A: To find the solution of the linear differential equation of first order y'+Py=Q, where P and Q are…

Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: Q-21 Solve the linear Differential dy + (x sin x + cos x)y = 2 dx equation x cos x-

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Q: dx I+ ylz

A: An equation which involves the derivative or differential coefficient is called differential…

Q: - Find the differential equation associated to the equation: y=C₁e sin x + C₂e cos x

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Q: Verify that the function y (cos( 6x)) is a solution to the differential equation y = 6 sin(6 9e

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Q: 2. Solve the differential equation dy 2y-cot x tan dx

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Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)x2y is an…

A: Here given differential equation as dydx=12x2yordyy=x2dx2

Q: Find the general solution for each differential equation.

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