10. A separable differential equation is also a homogeneous differential equation. sometimes true always false always true cannot be determine

Q: y" + 2y' + y = 7 + 75 sin 2x

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Q: A differential equation is considered to be ordinary if it has more than one independent variable.…

A: Given the statement A differential equation is considered to be ordinary if it has more than one…

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

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Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: 2. Determine the solution of differential equation de + -Q = 4 given that given that dt 10+2t Q(2) =…

A: We have to determine the solution of the differential equation…

Q: 6. Given a differential equation with coefficients linear in two variables. If the DE represents…

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Q: The general solution of the second-order differential equation y"-y-12y = 0 is: y = c₂e³x + c₂e-4x…

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Q: The particular solution to the nonhomogeneous differential equation y" + 4y' +5y = 10x + 3e-* %3D

A: The given differential equation y''+4y'+5=10x+3e-x. The particular integral is computed as follows,…

Q: If the general solution of the differential equation having 17 arbitrary constants, then the order…

A: In the solution of differential equation, its a rule that number of arbitary constant in solution of…

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

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Q: 1. Verify that for constant C the function ø(x) = + Cx is a solution of the differential equation 2…

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Q: 3. If the general solution to a second-order differential equation is given by cie + ce-5, find the…

A: In the question it is asked to solve the differential equations with initial values given.

Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: 5. Solve these differential equations by using the variation of parameters method. 4+36y=csc 3x (b)…

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Q: 2. Prove that the given first order ordinary differential equation (2x – y) dx – (x – 2y) dy = 0 is…

A: A detailed solution is given below

Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: 23. Find the particular solution of the differential equation (22 = 1 given that y 3 when y+2x/ dx

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Q: If the general solution of the differential equation having 14 arbitrary constants, then the order…

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Q: A differential equation is considered to be ordinary if it has more than one independent variable.…

A: Given the statement

Q: 21. Find particular solution of the differential equation- 2(x + 1)³ = dx (x+1) Y , given x = 0,…

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Q: 2. Use variation of parameters to determine the general solution of the nonhomogeneous linear…

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Q: (2ху? + уjdx — хdу %3D 0

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Q: If the general solution of the differential equation having 10 arbitrary constants, then the order…

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Q: Find the general solution of the given higher-order differential equation. du + + 6- drs dr4 12- dr2…

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Q: The Differential Equation y'+y=e* has a solution y=(x+C)ex C is an arbitrary constant. IF TRUE, show…

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Q: 5. xdy = (y + 2x³)dx

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Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

Q: 3. x? = Axy + By: A and B are arbitrary constants

A: Given: x2=Axy+By, where A and B are arbitrary constants.

Q: . Use separation of variables to solve the differential equation explicitly for u. du dt = 4 + 4u +…

A: topic:- differential equation

Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

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Q: If the differential equation is = ye", where x = 0, y = e. Determine the value of y when x = 1.…

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Q: Find the general solution of the differential equation y + 18xy* = 0 using separation of variables.…

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Q: 9. What is the particular solution of the linear differential equation ,3 Y = x° – 2xy; when x = 1,…

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Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: ).  Use separation of variables to solve the differential equation explicitly for u. du dt = 9 + 9u…

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Q: 8. Solve for the general solution of the differential equation using linear equation у' 3 csc x - у…

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Q: 4. When solving for the solution of higher order differential equations, the presence of x in the…

A: NOTE:Kindly repost the other question as a separate question.  When solving for the solution of…

Q: 1 The differential equation y' + x2 is separable. Select one: True False

A: Yes it is separable So it is true

Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: Find the general solution of the differential equation 2 = -3(y – 4). dt (Express numbers in exact…

A: We need to find the general solution of the differential equation- dydt=-3(y-4)dyy-4=-3dtIntegrating…

Q: obtained in factored form a linear differential equation with real constant coefficients that…

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Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

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

Q: (9))(y– 2x)y' = y %3D

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Q: y" – 2y' + y = -3 - x+x².

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Q: 3(a) Critically explain with practical examples on how a particular solution of a differential…

A: Note: Since you have posted independent questions. As per our policy we are allowed to solve only…

Q: If the general solution of the differential equation having 20 arbitrary constants, then the order…

A: Given: A differential equation having 20 arbitrary constant. Concept Used: Number of arbitrary…

Q: If the existence theorem is true but the existence and the unity theorem are not, then there is no…

A: Introduction:By using the principles of existence theorem and existence and unity theorem we can…

Q: For differential equation y'=t(y2 + 1) is the differential equation autonomous and does it have…

A: Given,  y'=t(y2+1)  If a differential equation is of the form y'=f(y) then it is called autonomous…