I. Find the general solution of the given differential equation. 1. y' + 2xy = x3

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

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

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Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

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

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Q: a. Classify and solve the first order differential equation y' = /2 +e'.

A: Answer  Linear differential equation is of the form         y'+Py=Q Where P,Q are function of t.

Q: Find the general solution of the differential equation. (Use C for any needed constant.) y' = 10VX y…

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Q: dy y3 dx x3 + xy² II

A: Given: - The differential equation is, dydx=y3x3+xy2 To show: - The given differential equation is…

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

A: Explanation of the answer is as follows

Q: 3. Find the differential equation associated to the equation: y = C₁x²e³* +C₁xe¹ +C₁e¹*

A: Note:- Since you asked multiple Questions ,As per our policy we can solve first question  for you…

Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

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: e. Cxy +C'x + 9 = 0

A: Cxy+C2x+9=0

Q: 4. Solve this linear differential equation by using the appropriate integrating factor +y =x - 1+

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: (d) y' – y = e"

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Q: Solve the given differential equation by separation of variables. dy e*y dx e-Y + e-3x - y

A: We will find out the required solution.

Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: by regarding y as the independent variable rather than x. Solve the differential equation. | 28. (1+…

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Q: Determine whether y 3 sin 2x + e-a is a solution to the differential equation y" + 4y = 5e

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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: What is the general solution of the given differential equation below? y' – 3y = 6

A: In the question we have to find general solution of the differential equation.   NOTE - As per…

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

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Q: 2. y-폼-y 1 ミ、 6x 3x2 ||

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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: 1. Obtain the differential equation associated with y=Ax2+Bx+C

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Q: Find

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Q: Find the general solution of the given differential equation 1 2 -y' + y = -x(secx)²y2 x2

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Q: Find the general solution of the given differential equation y" + y = 0

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Q: 1. y'- = xy2

A: Solution is given below:

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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Q: Solve the differential equation with the given initial condition. y' = y – e2ty4, y(0) = 1

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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: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: For the given non exact differential equation, determine the integrating factor. (x2 + 2xy - y2) dx…

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

A: Differential equations

Q: 3. Given that y = 1 when x=-1, find particular solution to differential equation dx dy – 3x²y² =…

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Q: y +y=}(e* – e*)

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

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Q: Determine an appropriate substitution and then solve the differential equation. xy' = y In(xy)

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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: 8. Obtain the differential equation associated with the given function: y = Cx² + C².

A: Proceed as shown

Q: y – 2)dx + (3x – y)dy = 0

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Q: 20.Find the particular solution of the differential equation x +1) = x3 – 2y, given x = 1 dx when y…

A: We have to find general solution of given differential equation with initial condition.

Q: I. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e² + c)

A: Given That : y-1=x(3ex+c) To Find: Differential Equation by eliminating the constant

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

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