10. Verify that the given differential equation is exact; then solve it. (8 cos x + In y)dx + dy = 0

Q: Consider the differential equation 3y" +y-2y = 2 cos t Which of the following is the general…

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Q: Find the value of the constant k so that the differential equation (6xy³ + cos y)dx + (kx²y² − x sin…

A: For the given Exact Differential (6xy3+cosy)dx+(kx2y2-xsiny)dy=0 value of k is 9 Hence option (A) is…

Q: 4) Find the general solution to the following differential equation y" + y = tan(t)

A: Find first homogeneous solution y''+y=0. The roots of auxiliary equation m2+1 is  m=±i Then…

Q: Find the general solution for the following differential equation: y" – 3 y' + 2 y = cos e-*

A: to find the general solution , consider the  equation y''-3y'+2y=0  the auxiliary equation is…

Q: 2ху y' y2 -x? (х — у)(4х + у)dx + x(5х — у)dy %3D0

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Q: Consider the following differential equation, cos(y) + (1+e-*)sin(y) dy dx Show that the general…

A: Given: cosy+1+e-xsinydydx=0 Use the variable separable method to solve the given differential…

Q: dy 7. dx cos(x + y), when x = 0,y =

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Q: 1. Find the solution of the following differential equation? Then find the particular solution with…

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Q: 1 dy -y =- cosx.y dx

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Q: 7. 1 (x dy – y dx) = 0 x² + y?

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Q: 1. Consider the equation (x + 2e + 2y) dx + (2x + cos y) dy = 0. (a) Show that the equation is…

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Q: (4) Find the general solution of the differential equation (D² + 2D + 5)Y = = cos ha

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Q: 1) Find the general solution to the following differential equation. dy +y (cotx) = 5e* dx %3D

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Q: y' + }xy = sin(x 4e¤2 y3 1

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Q: 1. Solve the following Exact Differential Equation : dx 3 1 (2?y3 - + y = 1 1+ 9x2' dy

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Q: a) Solve the following first-order differential equations: dy = -y 2x, given that when y=0, x=+2 dx

A: We have given  -y dy/dx = 2x when y = 0 and x = +-2

Q: 5) Find the general solution of the differential equation (D + 2D+ 5)y = e ² sin 12x.

A: Consider the given differential equation D2+2D+5y=e-x sin12x                …1 The above…

Q: It is known that y =A sin ωt is a solution of the differential equation yn + 16y =0. Find the…

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Q: x+y, 9- (e" + In y)dx+ (**)dy = 0 y

A: As per our guidelines, we are supposed to answer one question at a time.  Kindly repost other…

Q: verify that the given differential equation is exact and then solve it      (4x-y)dx+(6y-x)dy=0.

A: Here the given differential equation  Use the following definition

Q: Solve the given differential equation subject to the indicated conditions. y" - 4y = x + sin x, y(0)…

A: The given differential equation is y''-4y=x+sin x, y0=5, y'0=2y

Q: dy - (x- y + 1)'dx = 0

A: The objective of the question is slove the differential equations.

Q: dy 2 +y- 2x + 3 ご

A: We have to find General solution of given differential equation.

Q: find the general solution of the given differential equation. 7.y″ + y = 3 sin(2t) + t cos(2t)

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: 2) Solve the following differential equation 6y dx-x(2x'+y)dy =0

A: first we identify the given first order differential equation and find if it can be converted to…

Q: B) Solve the Bernoulli differential equation y' – y tan x + y2 cos x = 0

A: We have to solve the given Bernoulli differential equation y'-ytanx+y2cosx=0.

Q: What value of k would make the differential equation dy + In(x+1) = a'yk variables separable? O 2 O…

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Q: Solve the given differential equation and give the largest interval over which the general solution…

A: The given differential equation is dydx=y-42. solve the above equation as follows.

Q: You are given the differential equation (D+9)y=t cos(t), where y(0) 0 and %3D y (0)= The general…

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Q: (3) Solve the given differential equation (x* + y*)dx = xy®dy.

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Q: Find the solution of the following Differential Equations .by Exact sin(ß y)dx =-ßcos(ß y)dy

A: Let us discuss what is exact differential equation. An ordinary differential equation of the form…

Q: 4. Solve the following Second Order Differential Equation dy dy + 6- d.x 9. + 5y = 0 dx?

A: Given : 9d2ydx2+6dydx+5y =0

Q: 2. Solve the Second order differential equation d y dy 4+11 y = e“ sin 4x. dx

A: Given differential equation, d2ydx2-4dydx+11y=e-2xsin4x This can be written as D2-4D+11y=e-2xsin4x

Q: verify that the given differential equation is exact; then solve it. 37. (cos x + In y) dx +(÷+e" )…

A: Given, the differential equation is Verify that the differential equation is exact and then find…

Q: Solve the following nonhomogenous differential equation: d''''y/dx'''' + 2(d'''y/dx''') +…

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Q: 5. Solve the following second order differential equation dy + 9y = 4 – cos (3x) dx² by using the…

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Q: Solve the given exact differential equation (cos x+ In y)dx+ -+e' |dy =

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Q: 1) Find the general solution to the following differential equation. dy + y (cotx) = 5e* dx

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 4. Solve the following First Order Differential Equation: dy + 4y = x³ – - x dx

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Q: Solve the following differential equation I. Using Method of Undetermined Coefficients y" - y-2y= e*…

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Q: dy = 4x, = dx

A: Given differential equation is a variable differential equation

Q: Show that the given differential equation is not exact hence solve it æ?ydx – (x³ + y³)dy= 0 %3D

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Q: Solve the following differential equation using initial values. 1/2.yn+y'+y=0 ; y(0)=2 ,…

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Q: 3. Determine whether the given differential equation is exact. If it is exact, solve it. e (x – y3 +…

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Q: Solve the following Exact/Inexact Differential Equation. If it is inexact, then solve it by finding…

A: Given: 2xy-3dx+x2+4ydy=0; y1=2 Let P=2xy-3, Q=x2+4y Therefore, Pdx+Qdy=0 Now, dPdy=2x, dQdx=2x…

Q: Q4- Solve the following differential equation: (1+r)dy + (y-tan-¹(x)) dx = 0

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