Question 1 Show that y= Question 2 Given that 7 7 5 5 e -15x dy is a particular solution for +15y-21=0. dx dy (3x²y-cos x)+(x²-sin y) = 0. dx a) Test the exactness of the equation. b) Solve the given differential equation. Question 3 Find particular solution of the following initial value problem: 2.x dy xe dx -; y(0)=3. 2y (Hint: Apply tabular method to solve S 2x xedx)

Q: 2. Solve the following differential equation (2y + 1)e-vy = -e²+v sin z. Give the answer in the…

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Q: 1. xy + 4x²y= e¯®

A: The given differential equation is x3y'+4x2y=e-x rewrite the equation as…

Q: c) y' +y = 2 sin 3x + 4e-4x

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Q: Solve the following differential equation: - 5 - Y +x dy dx +y= 5 - U - 1.

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Q: Question 11 Solve the differential equation. y' + y tan x = cos x A y=x sin x+c sin x (B) y=x cos x…

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Q: Solve the given third-order differential equation by variation of parameters

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Q: 2. y' = (cos? x)(cos² 2y)

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Q: Solve the differential equation y + (tanx) y=cosx ? Ay=xsinx+Csinx By=xsinx+Ccos.x Ⓒy=sinx+Ccos.x D…

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Q: 2- Solve the following differential equation; dy = ycot(x) + y°csc"x - 1 dx %3D We observe that the…

A: The given differential equation is, dydx=ycotx+y2csc2x-1

Q: 3. (e* cot y + 2y csc y)y' = –e™

A: We Know that Integrating factor is defined as the function which is selected in order to solve the…

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: Given equation is 2z=x2a+y2b2p=2xa, where ∂z∂x=p and 2q=2yb, q=∂z∂ya=xp and b=yq2z=x2xp+y2yq2z=px+qy

Q: (¹ x sin(4) dy = (y sin [2)-1]dx. ; YLE) = x

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Q: 11) Solve the following differential equation: (D² - 2D + 1)y= 2 cos(x)

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Q: (x** ye) dx + zy dy

A: To Solve for the general solution of the following first order differential equations.

Q: xdy - (y + x² cos(x)) dx = 0

A: xdy-y+x2cosxdx=0xdy-ydx-x2cosxdx=0xdydx-y-x2cosx=0dydx-yx=xcosxFirst order linear diff. eq.

Q: Question 3: Solve the differential equation by first making the substitution u = y/t. ty² - t³ y³ y'…

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Q: e the differential equation by first making the substitution u = y/t. ² + y² ty LGC y = fit making…

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Q: Find the value of k so that the given differential equation is exact. (y + kxy4 - 2x) dx + (3xy2 +…

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Q: 3 dx - (3x sin y + 2y sin y − 2) dy = 0 -

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Q: 6) The variables x and y satisfy the differential equation X = y(1-2x²), dx and it is given that y =…

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Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: S following ordinary differential equations: 2) 2 2-}=-y3i COSX dx

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Q: Solve the given differential equation (D -3D+2)y=xe* +sin2x

A: We will find out the required solution.

Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x

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Q: 25. y"+y=2 x sin x

A: Let the non-homogeneous differential equation is,…

Q: 10) Solve the following differential equation: D (D+5) y = 0

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