If y, (x) = 2 is a particular solution of the y' + y² + (2cot² x)y – 4csc² x = 0 differential equation, then which of the following is the Bernoulli differential equation form obtained by the differential equation using a suitable transformation? dz а. dx + z(2 + cotx) = z² dz b. dx + 2z(2+ cot²x) =-z? dz с. dx + z (2 – cot?x) = z? | dz + z(2 – cotx) = -z? dx dz е. dx + 2z (2 – cotx) = z?

Q: (b) Use the substitution x = e' to transform the Cauchy-Euler equation x²y" – 4xy' + 6y = 3x² +…

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Q: Given partial differential equation i u, +2tu, = -sin x %3D ii u+2(u„)´ +u, = cos x %3D Based on the…

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Q: Verify that the indicated function y = g(x) is an explicit solution of the given first-order…

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Q: Given partial differential equation i u, + 2tu, = - sin x ii u +2(u,) +u, = cos x Based on the above…

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Q: The given differential equation is already in standard form, as the coefficient of the highest order…

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Q: dy_ y* +2xy³ – 3x²y² – 2.x³y 2.2 4 dx 2x²y² – 2x³y– 2xr* -

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Q: Use the separation of variables to find, if possible, product solutions (for λ = 0,2 = -a² and 2 =…

A: As per the question we are given a partial differential equation and we have to find its solution…

Q: y(4) + 64y = e* + cos 2x + In 3x + sin-14x + V5x Determine the complementary solution, yc, by…

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Q: 9. Use separation of variables to find, if possible, product solutions for the partial differential…

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Q: If x = a + 0 is a singular point of a second-order linear differential equation, then the…

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Q: Discretize the differential equation y" – 2y' + 4ty = 2t, y(-1) = -2, y(0) : -2 with step-size h %3D…

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Q: of two linear first-order ordinary differential equations: y1 = 2Y1 – 2y2, Y2 = Y1 – phase portrait…

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Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

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Q: Solve the exact differential equation (In y - y sin x-6e³x) dx + ( + cos x + 5 sec y tan y - 6y)dy =…

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Q: Verify that the indicated function y = 4(x) is an explicit solution of the given first-order…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Find the differential equation of the following function (x – 3y + 2)dx + 3(x + 3y – 4)dy = 0 x-1 a.…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: Note the following chain rule of differentiation : For a differentiable function y=1f(x)  , y' =…

Q: Determine the appropriate form for yp on the differential equation y"=9x^2 + 2x -1 a. y=Ax^4…

A: given the differential equation :

Q: Consider the differential equation y" - y' – 12y = 0. Verify that the functions e3x e4x form a…

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Q: Discretize the differential equation y" – y' + 4ty = 8(t – ), y'(1) = 0, y'(4) = 0 with step-size h…

A: Given ODE is : y"-y'+4ty=δt-52 , y'1=0 ,y'4=0  Since, we have the boundary condition of third kind ,…

Q: 9x2у" + 2у" +у %3D0 (d²y) |dy + 2у 3 х dx dx2 8²u 82u 8²u = 0 0 8x2 8x8y ' 8y² δχδν бу? +

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Q: If y, (x) = 2 is a particular solution of the y' + y² + (2cot²x)y –- 4csc² x = 0 differential…

A: The particular solution of a differential equation is always derived from the general solution of…

Q: Consider the ordinary differential equation y" + 4y -4y2 = -3t. Let y = y(t) and y2 =y'(t). Write…

A: Given : y'' + 4y' -4y2 = -3t

Q: у + Зу +2 у %3D 1+ e

A: Given the given differential equation is y"+3y'+2y=11+et

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Verify that the indicated function y = Q(x) is an explicit solution of the given first-order…

A: Solution : when y=125-x2y'=-125-x22×-2xy'=2x25-x22y'=2xy2thus in terms of x,2xy2=dydx

Q: 1) Consider a differential equation of the form [y +xf(x² + y³)]dx + [yf(x² + y³) – x]dy = 0, where…

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Q: (b) Use the substitution a e' to transform the Cauchy-Euler equation a*y" – 4xy' + 6y = 3x + In(a"),…

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Q: If y, (x) = 2 is a particular solution of the y' +y? + (2cot2x)y – 4csc² x = 0 differential…

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Q: Verify that the indicated function y = P(x) is an explicit solution of the given first-order…

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Q: Consider the differential equation (E): x²y" – 3xy' + 4y = x²Inx Given that y, = x² and y, = x²Inx…

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Q: Consider the partial differential equation u at' vith boundary conditions u(0, t) = 0 and u(7, t) =…

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Q: Solve the differential equation x" – 4x' – 12x = e3t – 2, x(0) = 0, x' (0) = 0 , by using the…

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: To verify that the function y=x+2√x+5 is a solution the given differential equation.

Q: One solution of the differential equation y"+9y=0 is y1= cos 3x use the method of reduction order…

A: Consider the given differential equation: y''+9y=0 y1=cos3x Here, the objective is to find the…

Q: Here is a homogeneous second-order linear differential equation, two functions y, and y2, and a pair…

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Q: Given that y, = 1, y2 = x2,y3 = e* are solutions of a third order differential equation (E). Then…

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Q: 3) Solve the differential equation z²y" – 2ry + 2y =z (1+ln z) by using a suitable transformation.

A: Given that, Differential equation is, x2y'' - 2xy' + 2y = x(1 + ln x) We have to find the solution…

Q: The differential equation y³y" = y²y' + 2y(y')² is transformed into a first order differential…

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Q: Show that the differential equation y²log y=xyp +p² can be changed to Clairaut's form by the…

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Q: Consider the Non-Homogenous differential equation: y" + 2y' = xe-5* + 3x² - 2 Given that y, C, +…

A: Given non homogenous differential equation and also given complementary function is given.  We have…

Q: Eliminate the arbitrary constants indicated in brackets from the following equation and form…

A: Given: The following equation, 1ez-x2y=ax2y2+by ;a,b.

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Show that the ordinary differential equation x’=(at+bx+m)/(ct+dx+n) a,b,c,d,m,n ∈ R, can always be…

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Q: Verify that the indicated function y g(x) is an explicit solution of the given first-order…

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Q: Verify that the indicated function y = P(x) is an explicit solution of the given first-order…

A: Given: y'=2xy2 and y=116-x2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.