x' = x + 2y y' = -x + 4y. ar solution associated with the initial conditions æ(0) = 1, y(0) = 0.

Q: Find the solution to y '= 3y satisfying y(2) = 1000.

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Q: y' = x³ (y-x)². + > |× $(x)=x y(s)=n Determine the interval ON which the solution exists.

A: The given equation is  Now,

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: Find the solution to x' = y y' = 12x + 1y if x(0) = 0 and y(0) = 8

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Q: Find the solution of y" – 2y' + y = 36 et with y(0) 6 and y' (0) = 5.

A: Given

Q: Find the solution to if x (0) = 0 and y(0) = 4. x(t) = y(t) = x' y' help (formulas) help (formulas)…

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Q: Solution: y1 = 1.450000000; y2= 2:085625000; y3 = 3:079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

A:

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.