A. Find the family of solutions of the following equation using linear differentic equations. 1. y' = cscx - y cotx = 6te2t + x(2t – 1) dx 2. t dt

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Q: find a linear homogeneous constant-coefficient equation with the given general solution. y(x)=Ae2x+B…

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Q: When is the derivative dy/dx of the parametric equations x(t)= 3cos t and y(t)=3sin t for Ost22n…

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Q: Q.1B) Solve the follwing diferential equation: 1 dy x dx siny + ycosy 2logx +1

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Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

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Q: 1. dy dx x + y x

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Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

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Q: Solve the following homogeneous problem in general: + 22 Py dx? dy + x – y = 0 dx dr3

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Q: Determine if the following differential equations are homogeneous: Estimated time: 10 minutes dy…

A: We have to determine if the given differential equation is homogeneous or not.

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Q: Show that the equation is homogeneous and find its solution. dy/dx = x+3y/x-y

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Q: Determine the solution of the following homogeneous DE: sec (G) -y ]dx +xdy

A: Given differential equation is x secyx - y dx + x dy = 0

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Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

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Q: dy 3. + Ay = w; y(0) = 0 and A> 0 dx

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Q: Given x = 2 cos t + 8 and y= 4 sint dx (i) dt dy (ii) dt dy (iii) dx ||

A: Givenx=2cost+8y=4sin2t

Q: dW w. if W=3x3+2y³ ; where x= e, y= cos 2t at t=0 dt Find

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Q: B. Solve the following equation using the determination of integrating factors. 2. y(4x + y)dx –…

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Q: 11. dw 12. J(Gu - 1)(3u* + 2) du J-scos z + 4 sec" x) dx 13.

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Q: Solve the following DE equation dy/dx=y^2/2x - y/x - 4/x              y(x)=4  Riccati DE Eqaution…

A: Since you have asked multiple problems, I answered first one. If you need solution of other problem,…

Q: find a linear homogeneous constant-coefficient equation with the given general solution. y(x)=A cos…

A: Consider the given general solution. y(x)=A cos 2x+ B sin 2x +C cosh 2x+ D sinh 2x

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A: Topic- differential equations

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A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: Consider the following. dy dx ex — У, (0, 1) %3D y | || 5+\/|| -4 ///+1 | 4 I| |-3+ (a) Find the…

A: dydx=ex-y ,   0, 1 On simplification, we get dydx+y=ex Now comparing with dydx+Py=Q, we get P=1…

Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: dx dy. If y =x is expressed with parametric equations such that - 6when x=1, what is dt dt 12 -6 -12

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Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: D. Identify the linearity of the following equations. y°dx + xdy = sin y dy 16. dzy +x- dt2 d?x 17.…

A: Given that:                                 NOTE: As per our answering guidelines, we can only…

Q: (f) 2 dy (2y+3) 4x+5 dx y(1) = 3

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Q: (a) Find the particular solution of dy, 2y cOS I y(T) = 0 dx

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Q: solve the first order homogeneous  equation  dy/dx =y/x +(x/y) ^2 , given y(1) =2

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Q: Which of the following equations is a linear differential equatio ду at A 4xycos(4t) = 0 +2x dx? dy…

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Q: What is the differential equation of the family of parabolas with their vertices and foci on the y –…

A: We need to find differential equation of the family of parabolas with their vertices and foci on y -…

Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

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Q: 2. 2y dx - x dy = 0

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Q: 13. 2xy dx + y“dy= 0; y(0) = 1. Answer: [2r² + y² = 1]

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Q: Find the general solution of the following IVP: (32²tany + 2) + (x³ sec?y – 1) = 0, y(0) = 0. %3D dz

A: Simplify the differential equation to exact form and integrate each terms.

Q: Obtain the general solution of the equation d'y dy + 3 + 2y = 10 cos 2x %3D dr dr Find the…

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

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Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y? y dy +

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Q: Obtain a solution to this linear equation. dx − (1 + 2x tan y) dy = 0

A: Given that: dx − (1 + 2x tan y) dy = 0

Q: . Find the family of solutions of the following equation using integrating factors found by…

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