1. (2 points) Solve the differential equations: (a) y'= Y 3x-y (b) (xsin-ycosdx dx + x cos Ydy = 0

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

A: It is given that the differential equation is 2y''+y'-y=x+5 The auxiliary equation is 2r2+r-1=0…

Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

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Q: O Solve the differential equation y' + y cot x = y* sin x.

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Q: y' – tan y-2x x+1 y+2 r+1 -

A: Given the DE is y'-tany-2xx+1=y+2x+1. Find the general solution of the DE.

Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: Determine the solution of the 1st Ordered Differential Equation: (x - y)(4x + y)dx + x(5x - y)dy = 0

A: We have to solve given problem:

Q: Explain how to solve a separable differential equation of the form g(y) y'(t) = h(t).

A: A separable differential equation is one in which the terms of two variables in the term can be…

Q: the indicial equation of the differential equation xy'' -x2y'+(1+2x)y=0

A: Question from differential equations.

Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: A tank contains 13 gallons of water to start, 9.5 gallons of water flow into the tank while 6…

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Q: Use Euler's method with 2 steps to estimate the value of y(1). (a) What is the value of the step…

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Q: d) Solve the differential equation of y"" + 4y' = sec 2x

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Q: Q3: Solve the differential equation: y "- yy "=(y ')'

A: Given that, y'''-yy''=(y')2 This can be written as, y'''=(y')2+yy'' Therefore, d(yy')=yy''+y'y' So…

Q: Q1 (a) Write 2 examples of nonlinear differential equations. (b) Identify the order of the following…

A: See solution below

Q: A solution of the Ordinary Differential Equation x?y'' - 2xy' + (x² + 2) y = 0, x > 0 is defined by…

A: 4th option is correct. y_p= xcos(x)

Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

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: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

A: