1b) Find an integrating factor and use it to find a general solution to the following equation: (y(x))+ 2y(x)e* + (y(x) + e*)y'(x) = 0 2

Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: By finding suitable integrating factors, solve the following equations: (a) (1-x?)y' + 2xy…

A: (a) Consider the given equation as equation (1) and obtain the integrating factor as follows.

Q: Solve y (t) + 5y (t) + 4y(t) = h(t); y(0) = 0, y (0) - 2 where h(t)%3D tfor0 s t S2 h(t) = (2t +…

A: A differential equation with the initial conditions is called an initial value problem. In this…

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

A:

Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

A: We have to solve for a linear equationPty''+Q(t)y'+R(t)y=S(t)

Q: Put the equation into the form x'(t) = g(t)h(x), and solve by the method of separation of variables.…

A:

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: Solve the following first order equations: (e" + y)dx + (2+x + ye")dy = 0, y(0) = 1.

A: First order linear differential equation

Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

A:

Q: Solve for Y(s) and Y(t)

A: Y(s)=s4−10s3+61s2−360s+9006s3−55s2+217s−1986​ (PLEASE SEE DETAILED INFORMATION ON THE EXPLANATION…

Q: ) Solve the equation (IVP) (1 +x²) – x(1+ 2y)y' = 0 y(1) = 0 %3D

A:

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

A:

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: y" (f) + (1 – t) y' (4) + e'y (t) = – 5t; y (0) = - 3; y' (0) = 4 into an in- tegral equation.…

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Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: For an equation y' + ty = 5t, find the general solution for y using method of integrating factor.

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Q: (b) Solve: (x*D² - 2XYDD' - 3y'D? +xD-3yD')z = x'ycos(Inx').

A:

Q: Use variation of parameters to solve csc(t) y = et. sec(t).

A: Given: Let us consider the given y=12-121y+csctsectet and solve by using a variation of parameters.