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Solve the differential Squation. 1 + 4 dt ut? + 14t2 du = +++ +C X...
Solve the differential equation. du dt 1 + 44 ut? + 14t2 with
Solve initial-value problem with u(o)= -4 du dt 35 + 7u + 5t + ut
Find the solution of the differential equation that satisfies the given initial condition. du dt 2u 2t + sec?(t), u(0) = -5 U = V2 + tan(t) + 25 X
Find the particular solution of differential equation -t du 2e dt at, initial condition, a 2(0)=1.
solve Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order differential equation d- du ( +54 + 60 = 10e-'u(t) dt 4 marks
QUESTION 1 (15 MARKS) a) Given 4'{+93}=LC }-( - siu (au) sin’au) sin(2t - 2u) du. Use the convolution theorem to determine the value of constant a. (5 marks) b) Using Laplace transform, solve the simultaneous differential equations dac dt - 4 =1+t, +2=t-1. dt given that x(0) = 0 and y(0) = 3. (10 marks)
solve please as soon as possible 24) Solve the ordinary differential equation: 1 + 2 dt? dt + 5y = e sint, given that when t=0: y=0, and x = 1
Solve the given system of differential equations by systematic elimination dx 20y dt dy = X + Z dt dz = X + y dt (x(t), y(t), z(t))
4. Show that the equation ut au bu du f(x, t) can be transformed into an equation of the form by first making the transformation ξ-x-ct. T-x + ct and then letting u weaf+dr for some choice of a, β.
2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1 2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1