y" + 9y' + 7y = e-2t ,t > 0[

Q: Find the Differential equation by eliminating the arbitrary constant y= A + bex

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Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

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Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Given problem:- Find the general solution of non-homogenous differential equation using Variation of…

Q: Determine the particular solution that satisfies the differential equation and initial condition…

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Q: 2. What is the integrating factor of the differential equation (x² -y²)dx + (x² - 2xy)dy = 0?

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Q: Find the differential equation by eliminating the arbitrary constant y= A + bex

A: Solution:-

Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

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Q: Find the particular solution to the differential equation. 4y2 dx = 3x2 dy    when x = 4, y = −1

A: The objective is to find the particular solution of the differential equation.

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Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: Determine the particular solution that satisfies the differential equation and initial condition…

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Q: find solution of order differential equation  dy/dx=cos2(x-y+1)

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Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

Q: The diffeterctial equation is y²dx+ 3xZy² dx + dy=0

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Q: Find the particular solution to the differential equation y' + ytanx = sin2x with the given boundary…

A: Given:         Differential equation y'+ytanx=sin2x            y(0)=1 This is in the form:…

Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: Find the general solution of xy' + y = y2lnx Bernoulli's differential equation.

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Q: Show that y - In(x +1) is the solution of the differential equation of (1+ x*)y= 4x':

A: Use the formula below to perform the differentiation .

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: Find the particular solution of the differential equation - ytanx e" secx that satisfies the initial…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: The given differential equation is, y''+2y'-8y=5e-2x-e-x. Obtain the homogeneous solution.…

Q: 2. Consider the differential equation y' -()y = 2+G) t If y(0) = yo, find the particular solution to…

A: Explanation of the solution is given below...

Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: Determine the appropriate form for yp on the differential equation y" = 9x^2 + 2x - 1 %3D

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Q: Determine the value of C for the given first order differential equation when x-2 and y=1. e#+v/ =…

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Q: The integrating factor of non-exact differential equation (x°y³ – ®)dx – (y6 – x³y)dy = 0 - -

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Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

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Q: 2ydx + x (x² In y – 1) dy = 0

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Q: A population (in thousands) grows according to the differential equation dy e ky(L-y), where the…

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Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: Consider the Non-Homogenous differential equation: y"-y= 6sinx Given that y. = Ce* + Cze-*, using…

A: Suppose we have second order linear differential equation as .  Consider are independent solutions…

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: To Determine -

Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

Q: y' + 2y = cos(2x)

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Q: Use the initial condition to find the particular solution of the differential equation. differential…

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Q: Obtain the general solution of the given Differential Equation using the Method of Variation of…

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Q: Find the equilibrium point(s) for the differential equation y" =y - y2 and determine their stability

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Q: Find a particular solution Y of the nonhomogeneous differential equation y'' + y' + y = 2 cost −…

A: Given a nonhomogenous differential equation y''+y'+y=2cost-sint

Q: Find particular solution of the differential equation dydx-2x+13=4x+1y , given x=0, when y=0

A: I have solved using integrating factor

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y =

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Q: For the differential equation y" --y' --= 0, find a particular solution which satisfies the initial…

A: To find the particular solution for the given differential equation which satisfies the initial…

Q: Use Teller's method to Solve the differential equation y-X JJ when h=0-2 s y(1)=2 Use The fifth rank…

A: We can solve this using Taylor method

Q: 2. y' + p(x)y = q(x)

A: