Given y"-25y=0, show that if y1=e-5t and y2=e5t are solutions then y=c1e-5t+c2e5t is also a solution.

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A: Exact differential equations

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Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, what are the values of a and b.

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A: Given: y''+by'+cy=0y1=e4t ,y2=te4t

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A: Lagrange's Method: Let us consider a standard form of the first order partial differential equation…

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Q: Solve through Bernoulli's Equation: * - y = xy O y-l +x – 1 = ce¯* O y + x – 1 = ce"

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Q: 3. Find a second solution to y" – 25y = 0, given one solution y1(x) = e5z. %3D %3D

A: Given differential equation is y''-25y=0 & y1x=e5x be one solution of the differential equation.…

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A: The solution is given below in the next step:

Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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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.