QUESTIONZ 2. {5 points) Find the general solution of the given differential equation y(4) – 2y3)...
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y = 0 Solve the given differential equation by undetermined coefficients. y'' + 4y = 2 sin 2x Solve the given differential equation by undetermined coefficients. y'' − y' = −10
Find the general solution of the given differential equation y(6) + y" =0 Find the general solution of the given differential equation y''' +3y" + 3y' + y = 0
3. Find the general solution of the homogenous differential equation. y" - 10y' + 29y = 0
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) = _______
1) Find the general solution of the given differential equationa) \(y^{\prime \prime}+2 y^{\prime}-3 y=0\),b) \(y^{\prime \prime}+3 y+2 y=0\),c) \(4 y^{\prime \prime}-9 y=0\),d) \(y^{\prime \prime}-9 y^{\prime}+9 y=0\).2) Find the solution of the given initial value problem and describe the behavior of solution as \(t \rightarrow+\infty\)$$ y^{\prime \prime}+4 y^{\prime}+3 y=0, \quad y(0)=2, y^{\prime}(0)=-1 $$3) Find a differential equation whose general solution is \(y=c_{1} e^{2 t}+c_{2} e^{-3 t}\).
(10 points) For the differential equation y(6) - 2y (5) – 3y(4) + 2y(3) + 10y" – 8y = 0. Find the fundamental solution set to the DE if the characteristic equation in factored form is given by (r – 2) (r2 + 2r + 2) (r - 1) (r + 1) = 0
D.E. (1) y Find the general solution of the differential equation ay - 25 y' + 25 y = 0. (2) Find the particular solution of the initial-value problem y .+ y - 2 y = 0; y(O) = 5, y (0) - - 1 (3) Find the general solution of the differential equation - NO OVERLAP! y. - 3 y - y + 3 y = 54 x - 3e 2x (4) Find the general solution of the differential...
5. Find a general solution to the differential equation using the method of variation of parameters y"' + 10y' + 25y 5e-50
Find a general solution to the differential equation using the method of variation of parameters. y'' +10y' + 25y = 3 e -50 The general solution is y(t) = D.
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =