Transform the differential equation 4y′+2y=t^(5) y(0)=9 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s) part b ) Therefore Y=

Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: Solve y""-2y"-5y'+6y=-12xe +2e¹; y(0)=2, y(0)=7, y"(0)=9 using the method of aplace transforms. Feel…

A: We will use the Laplace transform method to solve the above differential equation by taking the…

Q: Find dy/dx by implicit differentiation   √(x + y) =  1 + x2y 2

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Q: Differentiate. g(t) = 21t g' (t) =

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Q: Obtain general solution of ODE y''-y=exp(x) + cos(2x)

A: Step 1. Homogeneous Solution (y_h):We start by assuming the solution for the homogeneous equation…

Q: d²y dx² Use implicit differentiation to find dx dy 히근 and 4√y=x-3y II dx 이승

A: