Given the differential equation y" +9y = e-7t, y(0) = 0, y′(0) = 0 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = 1 (s+7) (s² +9) OF Now solve the IVP by using the inverse Laplace Transform y(t) = L¯¹{Y(s)} y(t) =

Q: 2) Use the Laplace transform to solve the differential equation y' + y' - 2y = -4; with initial…

A:

Q: Employ Laplace transforms to solve the differential equation of y"-2y'+y=3e¹* Given y(0)= and y(0) =…

A:

Q: y(t) = y" - 7y' + 6y = et + s(t - 7) + 6(t-9), y(0) = 0, y'(0) = 0 ) + ( [ ])2(x-7)+ ( [ 1) 2(t-1

A:

Q: Given the differential equation y'' + 3y' – 3y = sin(3t), y(0) = -2, y'(0) = 2 - Apply the Laplace…

A: Given that, the differential equation need to solve it using the Laplace transformation.

Q: Given the differential equation y"-4y'-y = 2 sin(5t), y(0) = 2, y'(0) = −1 Apply the Laplace…

A:

Q: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: Given the differential equation y'' + 5y' – 5y = - 4 sin(4t), y(0) = 2, y'(0) = 0 Apply the Laplace…

A:

Q: Consider the IVP y" +3ty'-6y=6,y(0)=0,y'(0)=0 (1).What is the Laplace transform of the differential…

A:

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c