Solve the exact differential equation (In y -y sin x-6e)dx+( + cos x + 5 sec y tan y - 6y)dy = 0 y (А) x In у+усos x - 2e3x +5 sec y -Зу?-с (В x Iпу+уcos x-2e3X+5 tany - Зу?-с (с) In хy - усos x - 2esX—5 sec y -Зу?%3с xIn у -усosх -2е3x+5 tan у -Зу?-Dс

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: Solve the differential equation subject to the indicated initial conditions. y" – 2 y' + 5 y = 1+t,…

A: Given differential equation is y''−2y'+5y=1+t and y0=0, y'0=4 We have to solve the given initial…

Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e-*. (a) Verify that yp = -3x +…

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Q: y'= (x²y- y)/(y+1);when x = 3, y = -1

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Q: Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is…

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Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: Solve the given third-order differential equation by variation of parameters. y''' − 6y'' − y' + 6y…

A: The given equation can be written as D3-6D2-D+6y=e4x. The auxiliary equation is m3-6m2-m+6=0. Using…

Q: Prove that the differential equation (x2 + 2ye2x) dy + (2xy + 2y2e2x) dx = 0 is exact and find its…

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Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

A: Given that the equation y=e5x-3x-x2. Find the differential equation satisfied by the given…

Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (1), can be…

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Q: 2. Prove that the given first order ordinary differential equation (2x – y) dx – (x – 2y) dy = 0 is…

A: A detailed solution is given below

Q: the differential equation y''+ 9y = sin(3t) + 2 cos(3t), y(0) = 2, y'(0) = 1

A: Given y"+9y=Sin(3t)+2Cos (3t) --1y(0)=2 and y'(0)=1.Auxilliary equation associated to the…

Q: 24.Use separation of variables to solve the differential equationdQ/dt=r(a+bQ),Q(0)=Q0, where a, b,…

A: dQdt=ra+bQ ,  Q0=Q0 By separating the variables, we get dQa+bQ=r dt Now integrating on both sides,…

Q: Determine the form of a particular solution to the differential equations. Do not solve. (a) x" – x'…

A: (a) The associated homogeneous differential equation is                     x''-x'-2x=0…

Q: Find the solution of the differential equation y'=xey-x^2 when y(0)=0.

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Q: Find the particular solution to the differential equation. x2e2y dy = (x3 + 3) dx    when x = 3, y…

A: We have to solve

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: Solve for Differential Equation y"-4y'+5y=0 when y(0)=0 and y'(0)=2

A: given differential equation y''-4y'+5y=0 with y0=0 , y'0=2 claim- to find the solution of…

Q: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

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: Determine whether each equation is a solution to the given differential equation. Fully justify your…

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Q: Suppose that a fourth order differential equation has a solution y=6e^(5x)xsin(x). Find the initial…

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Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

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Q: Find the general solution of separable differential equation when x=1 and y =1               dy/dx =…

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Q: Solve for Linear Differential Equation of Order n: y′′−2y′+y=7e^x+75sin(2x)

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Q: The differential equation x*y) - x y"- 5 y = 0 is a Euler-Cauchy equation. :Select one True False

A: The objective is to determine whether the given statement is true or false. Given differential…

Q: (x^2-4x-4)(y^2+1)dx+2y(x^3-2x^2+4x-8)dy=0; when x=4,y=1

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Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

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Q: If the differential equation is = ye", where x = 0, y = e. Determine the value of y when x = 1.…

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Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (i), can be…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: Determine the particular solution of the given differential equation: y = 2(3x +y) – 1. when x-0.…

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Q: Verify that the general condition satisfies the differential equation. Then find the solution that…

A: y''+9y=0 is the given DE with the general solution y=C1sin(3x)+C2cos(3x)...(1) To verify the general…

Q: x*y'(x) + (1+x) * y(x) - 2 = 0 Find the general solution of the differential equation. Since y(1)=…

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Q: Find the particular solution of the differential equation y’ + 7x = 0, at y = 0, x = 3. y = 63x2/2 y…

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

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Q: Find the particular solution to the differential equation. 2y2 dx = 3x2 dy when x = 2, y = -1 %3D

A: We first separate the variables2y2dx=3x2dy2dxx2=3dyy2then integrate both…

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Q: Solve for solution to differential equation. (2x-y) dx +(4x+y-6)dy =0

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Q: Find the general solution of the differential equation 8d2ydx2-6dydx+y=2x+40sin x

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Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (i), can be…

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Q: y -y = -8 te-t - 8 sin t %3D

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: Suppose that a fourth order differential equation has a solution y=−8e5xx cos(x). Find the initial…

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Q: The General solution of differential equation defined by: x2 y"-2x y'-4y=0 is defined by 1 y(x) = C,…

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Q: Is y = 2x² a solution to the differential equation 1/2 (x^2)y'' - xy' + y =0?

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Q: y= 2ax + bx^2

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Q: For differential equation y'=t(y2 + 1) is the differential equation autonomous and does it have…

A: Given,  y'=t(y2+1)  If a differential equation is of the form y'=f(y) then it is called autonomous…