
solve the differential equation ... Right now, I think it is in the general fourmation for linear

solve the differential equation ... Right now, I think it is in the general fourmation for...
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
I need help with this question of Differential Equation.
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Solve the given integro-differential equation by using the Laplace transform: (t) + 4' (t) = ['since sin(t – T) (t)dt, 4(0) = 2
find the general solution of the differential equation by using the system of linear equation. please need to be solve by differential equation expert. d^2x/dt^2+x+4dy/dt-4y=4e^t , dx/dt-x+dy/dt+9y=0 Its answer will look lile that: x(t)= c1 e^-2t (2sin(t)+cos(t))+ c2 e^-2t (4e^t-3sin(t)-4cos(t))+ 20 c3 e^-2t(e^t-sin(t)-cos(t))+2 e^t, y(t)= c1 e^-2t sin(t)+ c2 e^-2t(e^t-2sin(t)-cos(t))+ c3 e^-2t(5e^t-12sin(t)-4cos(t))
Provided that z(0) = 10, Solve the differential equation of: dz/dx = -z Secondly, solve the differential equation of: dz/dx = z^2 Now, state which of these is a linear differentiable equation? State which has solutions for every x greater than or equal to zero and provide explanation.
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (3t - 6)h(t – 2) - (3t – 12)h(t – 4), y(0) = y' (O) = 0 Y(8) -
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (4t – 8)h(t – 2) - (4t – 12)h(t – 3), y(0) = y' (O) = 0 Y(S) =
Q2 (10 points) 1. Solve the differential equation =-y given that y(0) = 10. 2. Solve the differential equation given that y(0) = 10. 3. Which of the above equations is a linear differential equation? 4. Which of the above equations has solutions for all t > 0? Explain.
Question 2: Differential Equations a) (3 points) Find the general solution to the equation. Use C,C1,C2 ... to denote arbitrary constants as necessary. y"(t) = sin6t + 20e b) (5 points) Solve the following separable differential equation for the given initial condition. y')= (1) = 0 c) (5 points) Solve the following first-order linear differential equation for the given initial condition. y't) + 7y - 3,y(0) - 1 d) (2 points) State the equilibrium solution and whether it is stable...
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Solve for the general solution to the differential equation below: y" - 5'- 2y + 2y = 0
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Solve for the general solution to the differential equation below: y" – V' – 2y + 2y = 0