Question

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

Answer #1

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),...

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

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)=

] Consider the autonomous differential equation y 0 = 10 + 3y −
y 2 . Sketch a graph of f(y) by hand and use it to draw a phase
line. Classify each equilibrium point as either unstable or
asymptotically stable. The equilibrium solutions divide the ty
plane into regions. Sketch at least one solution trajectory in each
region.

Find the general solution to the given differential
equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

Find the solution of the initial value problem
y′′+4y=t^2+4^(et), y(0)=0, y′(0)=3.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 4 minutes ago

asked 5 minutes ago

asked 5 minutes ago

asked 8 minutes ago

asked 13 minutes ago

asked 17 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 24 minutes ago

asked 26 minutes ago

asked 45 minutes ago