A) Solve the following linear differential equation 2 y' - y =0

Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

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Q: 10) 4xy dx - (6x² +y) dy so

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Q: Q.2: Solve the higher differential equation below; yiv – y = 2 cos x

A: yiv-y=2cosx The above differential equation can be written as D4-1y=2cosx      , D=ddx The Auxiliary…

Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

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Q: Find the solution of the differential equation y"+y' = sin x %3D

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Q: A: By using Linear equation solve the first order differential equation y' + sec(x)y = cos(x)

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Q: Assume that the rate of change in y is proportional to y. Solve the resulting differential equation…

A: Given  dydx=ky Points on the curve 3, 3 and 4, 6

Q: Solve the given differential equation by separation of variables. dy -4x - y dx

A: We have to form in a integrable form.

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

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Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

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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: Solve the given differential equation by finding an appropriate integrating factor to make it exact…

A: Given equation is the linear equation  of the form  dxdy+xP(y) = Q(y)  and integrating factor is…

Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

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Q: Solve for the General Solution of the given Differential Equation y' = y – xy³e- -2x

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Q: y = G, cos 3x – C, sin(-3x)

A: The general solution of a differential equation is y = c1cos(3x) - c2sin(-3x) We need to find the…

Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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Q: Find the solution for the second order differential equation y-4y = x sinh x.

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Q: Solve for the Linear Differential Equation: y' + y = 1

A: The given differential equation is y'+y=1. Solve the given differential equation.             The…

Q: 8. Solve for the general solution of the differential equation using linear equation y' = csc x- y…

A: To find the general solution of the differential equation using linear equation.

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

A: Given that: xdy-ydxy2=x3dx

Q: Find the solution of the following Differential Equations by Homogenous Equation 6) y'=+x y-x

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Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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Q: 24- Solve the following differential equation: (1+x²)dy + (y-tan-¹(x)) dx = 0

A: Solution to the differential equation

Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

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Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: а) у +у — 1 y' +y = 1

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Q: 1) y=x arccos - (c is an arbitrary constant), the lowest digit that satisfies Find the differential…

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Q: 6. Find the general solution of the following differential equation using variation of parameters.…

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Q: Find a single solution y(t) of the differential equation y′′=2

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

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Q: find differential equation of the following equation 1) y' = y-x y+x

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: y"+4y=x² sin 2 u

A: See the attachment

Q: Solve the given differential equation by separation of variables. y In(x) *- (1)* %3D Ap

A: Solution :-

Q: y" + 4y' = sec 2x

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Q: Determine the general solution of the given differential equation. y(4) + 2ylI + 2yl/ -x = 3e" + 2e™…

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Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² +…

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

A: We have to find

Q: +2) dx + (y? Inx) dy = 0, is exact differential equation. Select one: True False

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Q: Find the general solution of the differential equation: y′=(1+y)secx+tanx

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Q: Find the solution of the following Differential Equations by homogenous equation 7) y'=(y-x)

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

Q: Determine the integrating factor for the following differential equation y'=3x+6

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Q: 13. Solve the ivp differential equation: +y = e2x; y(0) = 0,y'(0) = dx

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin æ +…

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Q: Solve the given differential equation by variation of parameters. y" - y' = xe*

A: Given y"-y'=xex

Q: 1. Solve the differential equation dy y²sin(2x)sin²(x) = 0, y(0) = 1 dx - %D

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Q: dy_ y²sec² (-) tan (-) dx x2

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Q: 4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

A: Given: The differential equation is 1+x2dy+y-tan-1xdx=0 To find the general solution of the given…

Q: Solve the given differential equation by separation of variables. 2 y In(x) dx = (y + ¹)² X

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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.