Suppose a solution to a differential equation is given by: x(t)=5cos(2t)+12sin(2t) (a) Express the function x(1) in terms of x(t) = Acos(2t +) or x(t)= Asin(2t +ø). (b) What is the period and amplitude of this motion?

Q: Solve the following differential equation: x''(t)-2x'(t)=2e2tf(t);  x(0)=2, x'(0)=-1 where the…

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Q: Solve the differential equation by using the separable equation method 2 dx -sin 2t = 3 7 dt

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Q: on of period 2 pi in t. (x+sin r)(x

A: The differential equation is given as, dxdt=x+sin2tx-esint Let x=ft be the solution of the…

Q: For the differential equation y'' + 42y' + 152y = 8 cos(8x) Answer to the previous part: P(r) = r² +…

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Q: 1) Verify that the indicated function y = −(cos x) ln(secx + tanx) is an explicit solution of the…

A: First we will find y" Then put value of y" and y in   y"+y = tanx If we get  LHS =RHS then it means…

Q: solve the following first-order differential equations by first finding the integrating factor:…

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Q: у" + 25у %3D 5 tan? (5x) сos(5x) 2.

A: Given the DE is y''+25y=5tan25xcos5x. To solve this DE use the variation of parameters method.

Q: Differential Calculus Find the third derivative of the ff: 1) y x 1-ex 2) y = 2ex - 8x 3) y = 6ex -…

A: We have to find the third derivative of the given function.

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: Do the functions y1 = cos81 and y, = sin8t constitute a fundamental set of solutions of the…

A: Given a 2nd order linear differential equation y"+16y=0---1   We know that for the differential…

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: Obtain in factored form of a linear differential equation with real, constant coefficients that is…

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Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: Find the differential equation characterizing the family of curves described. Sketch at least three…

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Q: The degree of the differential equation (y") +y' – y = x is а. 2 с. 1 h no decree

A: We are asked to find the degree of the differential equation.

Q: Solve the separable differential equation. dy (1+y²) coshx dx 9+sinh x

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Q: (B) Solve the following differential equation: 3y cos 3x dx - sin3x dy = 0

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Q: ou are given the following differential equation:  (1/x4)(dy/dx) + (1/x2)y = x5, x > 0.  What…

A: Given differential equation A differential equation of the form is a linear differential equation…

Q: For each differential equation, indicate the order as a number. t³y"+t²y'+3y = sin(t) Order is:…

A: We have to find the order of the following differential equationsWe know thatThe order of 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.