Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are the constants a, b, c, d, and k?

Q: 8. y"-2y-15y=0 y(0)=5, y'(0)=-3

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Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

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Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

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Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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Q: The general solution of y' = X У can be written in the form = C

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Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

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Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: If u(x) = x3, then du = 3x2.

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Q: 20. '= 3 2 -1 2 1 -1, - (t) = -2t e² e³1 -4e¹-e-2t 2e3³t -e¹ -e-2t @3,

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

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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.