1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (wheret is a real constant)

Q: x'y" – xy' = Inx

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Q: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď²…

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Q: 4) The vertical displacement of a spring mass system from its natural length is described by d²y dy…

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Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

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Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

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Q: 20.Find the particular solution of the differential equation x (+1) - x-2y, given x -1 when y = 3

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Q: 4. The standard form of the first order linear differential equation x'y'+xy + 2 = 0 is

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Q: 1. Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

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Q: 1. The standard form of the general first order linear differential equation in y is 2. The linear…

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Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

Q: 9. The characteristics of the partial differential equation *3 = 0 ду a əx dy +2- дх ду + cos? when…

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Q: What is the particular solution to the 2² +3 with the differential equation dy da 3y initial…

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Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

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Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

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Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

Q: Show that y1 = sin x² and y2 = cos x² are linearly in- dependent functions, but that their Wronskian…

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Q: 2.) Find an explicit general solution y(x) for the homogeneous differential equation ry = y ln

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Q: State where in the ty-plane the hypothesis of the (non-linear) Existence and Uniqeness Theorem is…

A: Given: The given differential equation is y'=t-y2t+5y

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: we have y1, y2, .., Yn with domain R such that for any t E R , W (y1, y2, ... , yn) # 0. is there…

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Q: Find the general solution of non-homogeneous differential equation for y"+3y'+2y = 2020x which…

A: The differential equation is given as y''+3y'+2y=2020x Corresponding homogeneous differential…

Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

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Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

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Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: Determine the general solution of the differential equation y′′ - 4ky′ + 4k2y = ex, with k real…

A: In this question, concept of solution of differential equation is used. General equation of…

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

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Q: 4) The vertical displacement of a spring mass system from its natural length is described by dy…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Example 4: Form a partial differential equation by eliminating the arbitrary funct from Ix + my + nz…

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Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: 22/ for the differential equation ģ =X+y if ylo)=1 s ind y (ood) by Using Euller modibied method…

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Solve the differential equation dy/dx=5-x/y with the inital condition y(6)=-4.

A: We have to solve

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: Solve the Euler-Cauchy differential equation dy - 3x +4 y = In ² x – In x xp dx

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Q: 5. In the differential equation 2rydx + (y² -xy-0. what is -- 心

A: Solution

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

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Q: 3.) dy _ y (In(y)-In(х)) х dx

A: To solve the given differential equation.

Q: Solve the partial differential equation of ?2?????=6??2+3sin(?)+?−?cos(?), subject to the boundary…

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Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: (20) Determine the complete solution of the differential equation y" + 4y = 2cos2x subject to…

A: Solution: The objective is to find the general solution of the given differential equation

Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

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