Q1. Solve the following differential equations by separating the variables: (a) dx -x²dy = 0 (b) = 2x (c) xy' = 4y

Q: -(* +2) Solve for y = y (a) in the differential equation dy if y (0) = 1. No need to isolate y. %3D…

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Q: Find the particular solution for the differential equation y' = 4xe2x and y(0)=20.

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Q: Q4:A/ By using Exact equation solve the first order differential equation 2y² + yexy + (4xy + xexy +…

A: See this solution in below with details.

Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

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Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

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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: 4. Solve the differential equation by undetermined coefficients: y" +y' – 6y = 2.x. -

A:

Q: Given the differential equation y' = 4x y Find the next two Implicit derivatives of the differential…

A: The given differential equation is y'=4xy ............................................. (1)…

Q: Solve the given differential equation by separation of variables. dy yex -e-y = e-2x-y %3D dx

A: The differential equation is given as…

Q: Q5: Solve the differential equation y' y = 1 Subjected to the condition y(1)=e-1

A: we have to solve differential equation

Q: 2 (y+ 1) da- ydy = 0

A: Explanation of the answer is as follows

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

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

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

A: Here P and Q are two Arbitary constant ,so the heighest order of the differential equation is 2.

Q: Find the particular solution for the differential equation y' 4xe2x and y(0) =20.

A: Given that a differential equation and we find its particular solution . and also given that a…

Q: 10. Solve the differential equation by variation of parameters y" + 9y = 9 sec²(3x)

A:

Q: Q1- A: Solve the following first order differential equation: y' = x^(2) * y %3D

A: Differential equations of the form y'=f(x)g(y) is called a separable differential equation.…

Q: y'=6(y-2.5)tanh1.5x

A: Given differential equation is y'=6y-2.5tanh1.5x      ......1 or dydx=6y-2.5tanh1.5x

Q: 11. Solve the second-order differential equation y" – y' – 2y = 20 cos x using the method of…

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Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

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Q: Q-7. Solve the differential equation y = 1+ fip +..... for | 1 |< 1. dz dz

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Q: (3ху + 3у - 4) dx + (x+1)2dy %3D0

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Q: Solve the given differential equation by undetermined y' + y = x2 - 3x y(x) = %3D

A: Consider the differential equation 14y''+y'+y=x2−3x Write the auxiliary equation…

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: Solve the given differential equation by variation of parameters. y'' − y' = xex

A:

Q: Q3- Determine the general solution of the following differential equation: (x² – 2y²)dy + 2xy dx = 0…

A: Given differential equation is, x2-2y2dy+2xydx=0.

Q: Find

A:

Q: Solve the given third-order differential equation by variation of parameters. y"' + 16y' sec(4x) =…

A:

Q: 3. Determine the solution of the differential equation +-y x3 given that y (1)-A dx + R

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Q: 1. y'- = xy2

A: Solution is given below:

Q: (x4 + 2y)dx - xdy = 0

A:

Q: Solve the given differential equation by undetermined coefficients. y' + y = x² - 4x y(x) =

A:

Q: 2. Solve the given differential equation by separation of variables. x(1 + y²)/2 dx = y(1 + x²)!/2…

A: Topic- Differential Equation

Q: Solve the differential equation by variation of parameters. 1 8 + ex y" + 3y + 2y = t

A: We have to find the general solution of the given differential equation by Variation of Parameters.…

Q: I Using variation of parameters, solve the differential equation et y" – 4y' + 3y = 1+ er

A:

Q: Solve the given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t)

A:

Q: Q1. (i). Find a differential equation whose two-parameter family of solu- tions is given by y =…

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Q: Q1) Solve a first order differential equation. dy -x + Vx² + y² dx y

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Q: 2)By using y' = p substitution, solve the differential equation xy" = y' + x(y')².

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Q: Q5: Solve the differential equation y' – y = 1 Subjected to the condition y(1)=e-1

A: Differential equation is an equation which consists of Differential Coefficient in combination with…

Q: y – 2)dx + (3x – y)dy = 0

A:

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: A/ By using Exact equation solve the first order differential equation 2y² + ye* + (4xy + x² + 2y)y…

A: Topic:- application of differential equations

Q: 2. Solve the given differential equation by undetermined coefficients. y" + 2y = 2x + 9 – e-2x

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

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Q: Find the first five non-zero terms of the solution of the differential equation 2" + xz" + z = x² +…

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Q: Solve the given differential equation by undetermined coefficients. y" + y" = 8x2 y(x) = %3!

A: The solution is given as

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

A:

Q: Find the general solution of the differential equation: y' – 5y = xy. - Use lower case c for the…

A: The given differential equation is y'-5y=xy2 This can  be written as dydx-5y=xy2 Divide both the…

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.