Q2/ Classify the following equation as linear or not, and if not, what type of linearity it is: V; – c²v7x = 0 and verify that v = e¯*sin 2x is a solution for it if C² = 1/4 %3D

Q: Solve: 7x -9x%3D 2x-5 5-2x O A. x= 3 O B. x=-,-3 OC.x=--3 O C. x=-. D. x=--,3 E. None of the above 6

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: 2x273, if XEl f(x={x² +3, if XEl X2+1,if メフ f(t°+つ)=D3

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Q: - Find the linear equation that satisfies the following: f (3) = 10 and f(5) = 24 %3D I

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Q: dy = 2 yx + yx dx

A: Solve

Q: 10. S(2t² – 1)² dt

A: We have to evaluate the integral: 10. ∫2t2-12 dt We know the identity, a-b2=a2-2ab+b2 So by using…

Q: Solve the following IVP: (x²y+y +5x2 +5)Y =y2 +y-2; y(1)=2 dy dx

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Q: 9. S(1+3t)t²dt 10. S(2t2 – 1)² dt 11. fy²ydy

A: 9) Given integral is: I=∫1+3tt2dt Simplifying it: I=∫t2+3t3dt

Q: A particle moves in a straight line such that its acceleration when at position x (with respect to a…

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Q: fond solu tion of Bernoullidifferential equation %3D

A: Given y'+2xy=-xy4

Q: Find a real root of the equationx' +x - 1 =0 by iteration method.

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Q: frx) = x² -5x* , 5x * 3 %3D t X-intercept

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Q: population of a town has been growing linearly since 2000. The population t years since 2000 can be…

A: The population of a town has been growing linearly since 2000. The population t years since 2000 can…

Q: Q/ find the root of the equation by false position y = x3 – 6x² + 10x – 4 ɛ<0.001 for above…

A: Given,  The equation is  y=x3-6x2+10x-4 we have to find the root of equation using false position…

Q: erty' (t) = -8

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Q: Rewrite the following equation with the variables separated. ,2 y' + xVx²+1 = eYxx²+1

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Q: the optim

A: Let point on the curve y=x is (x,x). Then the distance between the points (x,x) and (5,0) is…

Q: Example: Given, y = 4cx .2 %3D Find orthogonal trajectores. Tikrit 1 Civil

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Q: Use the method of Variation of Parameters to solve the following DE: y'' – 2y" – 13y' – 10y = 2 +…

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Q: Solve the following first order equations: (a) (x²y² + 1)dr + 2r²dy = 0, use the substitution ry =…

A: We have to solve 1st order differential equation using substitution xy = u.

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

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Q: d²y/dx² of the function y=(5x² – 3)(7x³ + x)

A: The given function is: y=(5x2-3)(7x3+x)=5x2(7x3+x)-3(7x3+x)=35x5-16x3-3x To use the product rule for…

Q: gression equation to predict the y ducation: hat (Y)=5x+25. What is the y

A: Given question is :     Regression equation to predict the y  :  hat (Y) = 5x+25. what is the y…

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.