Use the Laplace transform to solve the system X +y -X = cost, x'+ 2y 0, x(0) = y(0) = 0. OA. x(t) cos(2t) + - sin(2t) + 1-t e,y(t) = 1 cos 2t 1 sin 2t - 4 4. 1 -3t - e OB. 1 x(t) = sin(2t) + e 2 cos(2t) + sin 2t 4 cos 2t – OC. 1 cos(2t) + - sin(2f) - –e',y() = 1 sin 2t + = e 4 x(t) cos 2t = - - - O D 1 sin 2t + 4 1 x(t) = cos(2t) 2 - sin(21) - e',y(t) = -- cos 2t + 2 cos(2t) + - 2 e',y(t) 1 sin 2t 1 t e x(t) = sin(2t) + cos 2t – 4 3

Q: 2. Let F(x) = x s sin (t2) dt. Find F'(x). (a) sin (x²) dx (b) sin (x²) (c) sin (x²) + C (d) 2x sin…

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Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: Question 3. Apply Laplace Transform to solve the following Integral Equation + 2√² e²-² x(t) = et +2…

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Q: Find the general solution of the inhomogeneous second-order linear ODE 2( 24" - 5' 3u)= 2(10 sinx)

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Q: Identify ALL linear differential equations. + (sin(t) + e' + 5x) + x = 0 d13 d²x + (1+t²) x = 10t…

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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.