1. y = x?ex + 4e*

Q: 5. Eliminate the arbitrary constant on the given equation: -4xy? + x°y2

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Q: Find the order, Degree and linear or Non-Linear Differential Equations 4 d*y y dx4 | for - x = 3.

A: Order of a differential equation is the order of the highest derivative  in the differential…

Q: If y = x2 – 2x and x changes from 2 to 2.01, find ∆y. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

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Q: What are the roots of the auxiliary equation for a homogeneous linear equation with real, constant…

A: Follow next step

Q: (D3 +5D2 +6D) у%3D24e -3х.

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Q: [2] Determine homogeneous the roots of the auxiliary equation y=x²-ecosx for a linear equation with…

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Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: 31 Solve by the Method of Variation of Parameters: y" – 3 y' + 2y = cos e t

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Q: se the method of variation of parameters to determine a particular solution to the given equation.…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: Solve the equation. (3x + 2y? + 2y³)dx + (2xy + 3xy² )dy = 0 An implicit solution in the form F(x,y)…

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Q: Q8. Solve the non-homogeneous Cauchy-Euler equation (a) x?y" – 2y = 3x².

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Q: Check whether the given first order linear diff equation is homogenous or exact or separable or none…

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Q: Q3. Given that yı = -3x²e¬3#, Y2 with constant coefficients, 7x* are solutions of a linear…

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Q: The function y=c1e-x+c2e-5x is the general solution of the homogeneous equation with constant…

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Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

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Q: If f(x)=Aekx , f(0) = 5 and f(3) = 10, find k. (SOLVE BY USING DIFFERENTIAL EQUATIONS

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Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: Verify that y = h(x) =- (C is an arbitrary constant, x # 0) is a solution of xy' = -y.

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Q: X’’ − 2x’ + x = 7et Write down the corresponding homogeneous equation and find its characteristic…

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Q: y" – 2y' + y = 1+a? 2

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Q: x²y" +xy' – 4y = 2x*

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Q: The following equation is a Homogeneous equation - (y/x form). Use the variable substitution u = y/x…

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Q: Obtain the homogeneous linear equation satisfied by the following given function 1. y = 4e2x + 3e¬x…

A: The homogeneous linear equation satisfied by the given equation: Part(1):   y=4e2x+3e−x⇒3e−x=y−4e2x…

Q: 18. Determine the roots of the auxiliary equation of y" + 3y" – 4y – 12y =

A: Follow the procedure given below.

Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

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Q: find a linear homogeneous constant-coefficient equation with the given general solution. y(x)=(A+…

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Q: Q/ Solve the differential equeion tx²y)dy=2xydx

A: The Given differential equation is: (x2-y2)dy = 2xy dx Rearranging the differential equation:…

Q: Find a homogeneous linear equation with constant coefficients with the given general solution (a) y…

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Q: Find an integrating factor and solve the equation 4x y' = e¹x + 8y - 1.

A: Solution of given question is written in below steps.

Q: A. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Distinct Roots) 5. (4D4 + 4D3 –…

A: Given: (4D4 +4D3 -13D2  -7D+6)y To find the auxiliary equation.

Q: Determine the general solution of y(1) = x - 2y cot (2x)

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Q: y" + y = sec (x)

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Q: A. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Distinct Roots) 3. (4D3 – 7D +…

A: Given differential equation is

Q: find a second independent solution of the given equation.…

A: Rewrite the given differential equation, in the form Divide the given differential equation with x2…

Q: Solve for the 2nd order nonhomogeneous linear equation: y"+12y'+37y=10e-4t     ; y(0)=4,  y'(0)=0

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Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: 2xy y' + 2x² x' = y² x'

A: Given: 2xyy' + 2x3x' = y2x' ⇒2xydy + 2x3dx = y2dx ⇒2xydy- y2dx=- 2x3dx

Q: List the roots of the auxiliary equation for a homogeneous linear equation with real  constant…

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Q: \y' = (y – 2) cotx -lve it as separable equation and verify your swer by solving it as a linear…

A: Topic = Differentail equation

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 3. (4D4 + 4D3 –…

A: To find the solution of homogeneous differential equation 4D4+4D3-3D2-2D+1y=0, find the factors of…

Q: y dx + (3x – xy + 2) dy = 0 -

A: As per the instruction, we will be solving only the first one. For (4),We will solve it by Exact…

Q: 1. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Distinct Roots) 2. (D3 + 3D? -…

A: We have given the third-order homogeneous differential equation as D3+3D2-4Dy=0. Here, the auxiliary…

Q: Solve the given second order differnetial equation using variation of parameteres: y'' -4y =xex

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Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: y" + y = sec (x)

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Q: 2. Determine whether or not y = Ce2t + Cze-4t + (4/7)e3t is a solution to the differential equatior…

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Q: What are the roots of the auxiliary equation corresponding to the DE y" + 3y" + 3y' + y = 0? Write…

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