1. Solve the differential equation to find y: (1+ x)2+y= Vx

Q: Q2-Solve the differential equation dy = - y xcos² (-) dx

A: I am attaching image so that you understand each and every step.

Q: Figure out the order and degree of differential equation that can be formed from the equation V(1 –…

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Q: Solve and find the domain for the differential equation: (x2y2)dx + xydy = 0 , y(3)=-6

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Q: 9 Find the general solution to the differential equation y' where x > 0. y = +C

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Q: 1. Solve the given differential equation (2xy*e" + 2xy" + y)dx+ (x*y*e" – x*y² - 3x)dy= 0

A: The solution is given as

Q: Solve the differential equation (y-x2) dx + (x2 cot y -x ) dy =0

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Q: y'dy-(4y + 48x kdx = 0

A: Let us consider the linear non homogenous  first order differential eqaution of the form  dydx+p(x)…

Q: (6) Solve the homogeneous differential equation (x – y)dx – 2xy’dy = 0 - |

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Q: _6// Solve the differential equation 2y³dx – (yx? + y³)dy = 0

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Q: 2. Solve the Bernoulli differential equation y' +y = y2

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Q: 1) Solve the differential equation x² + y² ) dx - :- (ryVx² + y²) dy = 0.

A: the given differential equation is: x3+y2x2+y2 dx-xyx2+y2 dy=0 we have to solve the given…

Q: Solve for the general solution of the given first-ordered Linear Differential Equation y' = x – 4xy

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Q: 3. Solve the given differential equation xy dy - (x2 +y)dx

A: The given differential equation is  xydy - (x2 +y2)dx = 0 (x2 +y2) dx - xydy=0

Q: 4) (y + x² ) dx = xdy Find the general solution to differential equations

A: We have given a differential equation   y + x2 dx =  x dy ydx + x2 dx = x dy x dy - y dx = x2 dx

Q: B- Solve the differential equation (D² +1) y = x² cos 5x

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Q: The differential equation y' = Vx+y+1–1 has the solution:

A: We need to solve the differential equation given by y'=x+y+1-1 The solution is given below.

Q: Solve the linear differential equation of y' – 2xy = r.

A: Answer :The given differential equation is y'-2xy=xIt can be written as dydx-2xy=x    -(1)

Q: Solve the differential equation (1 + y² + xy²) dx + (x²y + y + 2xy) dy = 0

A: Solve the exact differential equation  1+y2+xy2dx+x2y+y+2xydy=0

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

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Q: Q-4 Find the general solution of the Differential equation (D² + 5)y= sin z

A: Given differential equation is: D2+5y=sinx General solution for the non homogeneous second order…

Q: 1. Solve the differential equation to find y: dy (1+ x)+Y = VX dx

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Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

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Q: 1. Find the differential equation whose solutions correspond to the following equation  y = C1e−x +…

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Q: 5. Find the general solution to the differential equation e-y" = (y')? (where y' = ) dx

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Q: III. Find the particular solution of the differential equation and f(3) = 7, y-4 %3D dx

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: y' +- y = 0, y(1) = 0

A: Given : y' + y/x - √y = 0, y(1) = 0

Q: 1. Obtain the Differential Equation from the given general solution. y = C + C2x + C,x² + C4e 2 +…

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Q: Solve the differential equation y’=xsqrt(y); y(0)=1

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Q: Solve the given differential equation by undetermined coefficients. y" + y² + y = x² - 5x y(x) =

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

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Q: (5) Find the general solution for the exact differential equation (x² – 4xy – 2y2)dx + (y? – axy –…

A: The given differential equation is x2-4xy-2y2dx+y2-axy-2x2dy =0

Q: b. Solve the exact differential equation (9x* +5x*y*)dx +(4x°y° -7y° )dy = 0.

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Q: (5) Find the general solution for the differential equation (x² – 2xy – y²)dx – (x + y)²dy = 0.

A: It is a first order non linear ordinary differential equations and also it is a exact equation…

Q: 2. Find the general solution of the differential equation e-ty'- y = 2e-t+e".

A: Differential equations

Q: (x - y) dx +(3x + y) dy = 0

A: The given differential equation is: (x-y)dx+(3x+y)dy=0...(1)

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve the exact differential equation: (a?y3 - 1 dr+y?dy 0 1+ 9x2

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Q: I. Solve the differential equation. (y-1ldv +x Cx+1)dy = o

A: Solution:

Q: 4. Find the solution to the differential equation ä + 3i + 2x = 0 x(0) = a, i(0) = b

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Q: (D² – D − 2)y - COS X

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Q: 5 Find the general solution to the differential equation y - where x > 0. y = +C

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Q: 2. A solution for the differential equation is y = Pe-3x/2+ Qe¬x!2.

A: Let's find.

Q: 2. Determine the solution x(t) of the differential equation * + 2x + x = 0, x(0) = 1, *(0) = 1

A: Given differential equation is: x''+2x'+x=0 And the initial conditions are x(0)=1 and x'(0)=1 The…

Q: (e– 1)y' = 2 + cos.x -

A: Let us consider the differential equation of the form dydx=f(x)g(y) Rewrite the equation as…

Q: 1. Solve the differential equation (x+y)'dx+(2xy +x -1) dy =0 subject to the initial condition y(1)…

A: Compare with exact differential equation and then check exactness

Q: y' - 5y = -xy, y(2) = 1

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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.