5*.) Find the general solutions of the following linear differential equations: a) y +4 y = 2 e-4z b) y' +y tan(x) = sin(r) c) ry +2y 2 x

Q: B 4a X A 66° 20

A: The given figure is -  We have to find the value of 'x'.

Q: Which of the following differential equations can be solved by utilizing the method of undetermined…

A: The method of undetermined coefficients is used only when the function on the right hand side is a…

Q: Use the steps (a)-(c) below to solve y"+ 2y + (e - 3)y = 0. Define a new independent variable z = e"…

A: Consider the given differential equation:

Q: 1. Determine a general solution of the differential equation: y" + 4y + 5y = 200 sin t

A:

Q: 141: Find the general solution of the given ordinary differential equations. a) y" +4y' + 7y = 0 b)…

A: a) y"+4y'+7y=0 Auxiliary equation is  m2+4m+7=0⇒m=-4±16-472⇒m=-4±232⇒m=-2±3 So, the general solution…

Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Phase portrait of x''+10x'+24x=0 Phase portrait of x''+2x=0

Q: 17. Determine the differential equation whose general solution is y = C,Sin3t + C,Cos3t . d? y - 9y…

A: Topic = Differential equation

Q: 1. a) Solve the following differential equations: ydx x i) -1 (tan-¹x) dy = ydx x² +1 (In x)dy, b)…

A:

Q: 2. Verify that the given differential equations are exact and solve the equations: (a) (4x³y - 15x²…

A:

Q: 4. For the given differential equation write a particular solution with unde- termined coefficients.…

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Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

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Q: 3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0,…

A: As you didn't mention the question number to be solved so I solved two questions. For remaining…

Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: s) Are the following differential equations of homogeneous degree? (You have only one attempt!…

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Q: (a) Derive (7), and(), (b) Show that P = P(T, V) then the dP is an exact differential.

A: For the given function P=RVV-B-AV(V+B)T1/2 To find the partial derivatives and To prove dP is

Q: Solve the following differential equations of Dyy = 2 y-x; 2- yy+ %3D

A:

Q: State the order of the given differential equation. (1-x) y" - 4xy + 5y = cos x d³y +y=0 dx³ a) b)…

A: a) The given differential equation is (1-x)y''-4xy'+5y=cosx. Since y'' is the highest order…

Q: Q.1) Evaluate psec(x) 3cos(x) dydx Q.2) Evaluate -dzdrdy 1+y Q.3) Find the solution of the following…

A:

Q: Find the solution to the differential equation that satisfies the stated condition. sin (5x + T),…

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Q: show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given…

A: Given differential equation y''+4y=0  y1(t)=cos(2t)     , y2(t)=sin(2t)

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: (2xy - y² + y)dx + (3x² - 4xy + 3x)dy = 0

A: The given differential equation is