y(x) = C,e*+C,e*cosx is a solution to the equation y"-3y"+4y'-2y 0 for any pair of constants (C, ,C) 2) Show that there is no pair of constants (C, ,C,) for which y(x) above satisfies the following IC's y(0) = 1, y'(0) = 0, y"(0) = 0

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A: We will verify the given statement.

Q: Find y' given 5y² - 8x4 + 3 = 0, and evaluate y' at (x, y) = (1, 1).

A: Given query is to find indicated derivative

Q: Consider that Let the solution of equation y₁ = x² y2 = 3x² - y3 = 4x-2 2 x² x²y" + xy' 4y = 0…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

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A:

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Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

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Q: d'y dx +8y = 2x – 5 + 8e **, y(0)=-5, y'(0)=3. y"(0)=-4

A: Given the differential equation            y'''+8y=2x-5+8e-2x with initial conditions y(0)=-5,…

Q: Find a solution of x = y²_ (a) (0, 1) 1 1-xec y = (b) y = dy dx (0, 0) y = (c) (-1/2-1/2) (d) (2,…

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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.