Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y_1, y_2, ... for y1, Y2, ... .) 1 0 0 1 - 25 0 Y1 Y2 Уз Does the indicated general solution satisfy the system? Y1 = C1 + Cz cos(5t) + C3 sin(5t) 5C3 cos(5t) – 5C2 sin(5t) -25C2 cos(5t) + 25C3 sin(5t) Y2 = Y3 = Yes O No

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A: We will convert the given system to a system of first order differential equations in matrix form.

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A: Given Differential equation  .Transform into system of first order differential equation .

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A: i just substituted the given variable in a proper way in given second order system.

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A: Every system of differential equations can be written in vector form also.

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Q: X= [+] -3 1 X × ² = [ 2² -4 ] X X2-26-561 est

A: For the differential equation, to checkand the set is fundamental set of solution.

Q: please solve asap

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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.