y" – 4y' – 12y = sin(3t)

Q: xydy – (y 3x2) dx = 0 –

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Q: Find the general solution to the following nonhomogeneous differential equation using the method of…

A: The given nonhomogeneous differential equation is y''+4y=cos3x. Calculate the general solution of…

Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

Q: Find afunction yp that is a solutionto the differential equation,y′′+y′=2e2x+cos(x).

A: To find the solution y"+y'=2e2x+cosx

Q: Find the equation which satisfies the separable differential equation dy – 15x dx with the initial…

A: Given dydx=-15xy    y(1)=-5To find solution:

Q: dy dx

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Q: Consider the autonomous first-order differential equation dy/dx = y – y° and the initial condition…

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Q: dy = (x³ – 2xy)dx

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Q: 2. Find the golution for the following differential equation using integrating factor. i + ty - 1 =0…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given differential equation

Q: Evaluate the given differential equation (3siny – 5x)dx + 2x°coty dy = 0

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Q: Use Frobenius method to find the first three non-zero terms for the following differential equation:…

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Q: Consider the differential equation dy (t – 81) + 5ty = sin(t) with y(1) = 2t. %3D There exists a…

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Q: y = Ae + Bxe* %3D

A: given  y=Aex+Bxex we have to form the differential equation .

Q: y' = 2y + x(e3x – e2x) y(0) = 2 %3D

A: To solve the following problem by 4 step   Find yc Find p.i. yp  The general solution = yc + yp…

Q: Find the general solution for the following differential equation using the method of dy 36y =…

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Q: y = c, sin wt + c2 cos wt

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Q: Compute the following first-order differential equation i. cos x dx +y = sin x , subject to the IVP…

A: Given first order differential equations Using linear differential equation Form

Q: Consider the following differential equation: (12xy3+32ysen(xy)cos(xy))dx+N(x, y)dy=0 Calculate N…

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Q: Obtain the general solution for the following differential equation using Separation of Variables…

A: Using method of seperation of variables

Q: Classify the following differential equation: y + y cos(2nt) – 2t² = 0 Order 1 Linearity nonlinear…

A: Solution:-

Q: Find the general solution to the given differential equation. ( Use C for the constant of…

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Q: Obtain the general solution of the given differential equation: dy = cos²xcosydx

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Q: Given a differential equation xy'+y = (xy) In x with initial an 1 condition y(1)=;. Calculate the…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dx=x9y dy. Rewrite this as y dy=dxx9.

Q: (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Given differential equation is  1+exydx+exy1-xydy=0 Which is in the form of Mdx+Ndy=0. where…

Q: 'dy = (cscx- ycotx)dx

A:

Q: dy = (x – 3y)dx

A: The given differential equation is: dy = (x-3y)dx We need to find the integrating factor for the…

Q: xydy - (y – 3x²) dx = 0

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Q: (1– 3x)dx y –dy = 0.

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Q: 3. Solve the following higher order differential equation given that y() = 0, y'(품) %3D2 dy + y = 0…

A: The solution is given as

Q: Solve the following higher order differential equation given that y() = 0, *.... dy + y = 0 da?

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Q: Consider the following first order differential equation dy dr -- 4y = 2ry What is the asymptotic…

A: The given differential equation is, dydx - 4y =2xy2         ............1 Divide equation (1) by y2…

Q: Solve the differential equation with the initial condition. Show all of your work. dy y? with y(0) =…

A: Detailed solution is given below.

Q: The appropriate integrating factor for the following differential equation (3xy + y²)dx + (x² +…

A: The given differential equation is 3xy+y2dx+x2+xydy=0....(1) We will find the integrating factor of…

Q: . Find the golution for the following differential equation using integrating factor. +ty-1 0 dt

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Q: The appropriate integrating factor for the following differential equation (3xy – y?)dx + x(x - y)dy…

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Q: fip dr 3. re?y dy In(x)

A: This Bernoulli's differential equations  Note Here initial value not given so i solve  this as…

Q: Let c be a constant. For the following differential equation: dy - y = x dx In which of the…

A: Given differential equation is dydx-y=x      1 We know that Isoclines are given by putting the…

Q: Show that the coefficients of the given differential equation are homogencous and solve the given…

A: Given, The differentiating equation  x2+2y2dxdy=xy   and  y-1=1 We have to show the coefficient of…

Q: Solve for the general solition of the followimg differential equation using FOLDE 2. (y - x + xy…

A: Given DE is  (y - x + xy cotx)dx + dy = 0.......(1) We solve this DE.

Q: Consider the following Bernoulli differential equation, y'y' + 2xy = e3" y°. ,6

A: Given Bernoulli Differential equation y5y'+2xy =e3xy6 To do  Find the general solution   Standard…

Q: +2) dx + (y? Inx) dy = 0, is exact differential equation. Select one: True False

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Q: Determine the integrating factor for the following differential equation y'=3x+6

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Q: obtain the solution of the following differential equation y'=cos^2x cosy

A: Given differential equation is: dydx=cos2xcosy Use variable separable to get solution of…

Q: What should be A for the exact differential equation of ry + A 2Ay – x -dy y? Moreover evaluate the…

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Q: Is the differential equation exact or non-exact. 6x^2y dx+4x^3y dy=0

A: Exact or non exact differential equation

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.