Question

Differential Equations. ty'+3y=e^{t} /t with t > 0
and initial data y(1) = 2

Answer #1

solve the differential equations by series of potentials:
a)y''(t)=ty(t)
b)y(t)''+ty(t)'+2y(t)=0

Find the solution of the given initial value problem.
ty′+3y=t2−t+5, y(1)=5, t>0

for y(t) function ty'' - ty' + ty = 0, y(0)= 0 , y'(0)= 1
solve this initial value problem by using Laplace Transform.

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

Solve the initial value problem
3y'(t)y''(t)=16y(t) , y(0)=1,
y'(0)=2

y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a
non-homogeneous linear second-order differential equation
withnon-constantcoefficients andnotof Euler type.
(a) Write the Laplace transform of the Initial Value Problem
above.
(b) Find a closed formula for the Laplace transformL(y(t)).
(c) Find the unique solutiony(t) to the Initial Value
Problem

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''-y=delta(t-3), y(0)=0,
y'(0)=1

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''' +y' =0, y(0)=1, y'(0)=2, y''(0)=1

Solve the initial-value problem:y′′+y=et(1+u1(t)),y(0) =y′(0)
=0.

Given the second order initial value problem
y′′−3y′=12δ(t−2), y(0)=0, y′(0)=3y″−3y′=12δ(t−2), y(0)=0, y′(0)=3Let
Y(s)Y(s) denote the Laplace transform of yy. Then
Y(s)=Y(s)= .
Taking the inverse Laplace transform we obtain
y(t)=

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