Quasilinear equation

See attachment

Quasilinear

The two problems are attached. Thank you once again.

Differential equations

Hi, Please help solving these problems section 4.3 # 4,16,22,34,38 See attached The auxiliary equation for the given differential equation has complex roots. Find a general solution. Solve the given initial value problem. Prove the sum of angle formula for the sine function by following these steps.

Differential equations

Hi, Please help on these problems section 4.4 # 2,4,6,8,12,18,24,28 See attached Decide whether or not the method of undetermined coefficients can be applied to find a particular solution. Find a particular solution. Determine the form of a solution.

(1) Find a general solution to the following non homogeneous differential equation: y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2 (2) Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equations (a) y'' - y' + y = (e^t + t)^2 (b) y'' + y' + y = e^t + 7 (c) y'' - 2y' + 3y = cosh t (3) Find general solution to the following differential equations: y'' + 4y = sin q - cos q y’’ + y’ – 12 y = e^t + e2t – 1 y'' - 4y' + 4y = t^2 e^t - e^(2t) (4) Find a particular solution to the given higher order differential equation: y^(4) - 5y'' + 4y = 10 cos t - 20 sin t

Please help working on these attached problems section 4.5 #6,10,12,14,20,28,36,38 Thanks (6) Find a general solution to the following non homogeneous differential equation: y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2 Decide whether the method of undetermined coefficients together with superposition ...continues

Variation of parameters

Hi, Please help on solving these problems section 4.6 # 2,10,14,16 See attached Find a general solution to the differential equation using the method of variation of parameters.

Differential equations

Please help solving these problems section 4.7 # 4,6,12 section 4.8 # 2,6,8,12 section 4.9 #4,8,12 see attached Find a general solution to the given Cauchy-Euler equation... Using the paradigm, what are the inertia, dampness, and stiffness.... Use the energy integral lemma.... Use reduction of order to solve....

Elimination and differential equation

Please help on these section 5.2 # 4,8 see attached Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.

Differential equation

Please help on these problems section 5.4 # 2,4,8,12,28,33 Thanks attach is the reference Verify that the pair s(t), y(t) is a solution to the given system... Find the critical point for the given system... Determine the integral curves for the given system.... Solve the phase plane equation...

Initial-Value Problem

Please see the attached file for the fully formatted problem. Solve the IVP: y'' + 4y' +13y = 13t2 -5t +24 +e^-2t(sin 3t)