Question

Solve the Initial Value Problem:

- dydx+2y=9, y(0)=0
- dydx+ycosx=5cosx, y(0)=7d

- Find the general solution, y(t)y(t), which solves the problem
below, by the method of integrating factors.

8tdydt+y=t3,t>08tdydt+y=t3,t>0

Put the problem in standard form.

Then find the integrating factor,
μ(t)=μ(t)= ,__________

and finally find y(t)=y(t)= __________ . (use *C* as the
unkown constant.)

- Solve the following initial value problem:

tdydt+6y=7ttdydt+6y=7t

with y(1)=2.y(1)=2.

Put the problem in standard form.

Then find the integrating factor, ρ(t)=ρ(t)= _______ ,

and finally find y(t)=y(t)= _________ .

Answer #1

Solve the Initial Value Problem:
a) dydx+2y=9, y(0)=0 y(x)=_______________
b) dydx+ycosx=5cosx,
y(0)=7d y(x)=______________
c) Find the general solution, y(t), which solves the problem
below, by the method of integrating factors.
8t dy/dt +y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)= ,__________
and finally find y(t)= __________ . (use C as the unkown
constant.)
d) Solve the following initial value problem:
t dy/dt+6y=7t
with y(1)=2
Put the problem in standard form.
Then find the integrating...

Solve the initial value problem
2(sin(t)dydt+cos(t)y)=cos(t)sin^3(t)
for 0<t<π0<t<π and y(π/2)=13.y(π/2)=13.
Put the problem in standard form.
Then find the integrating factor, ρ(t)=
and finally find y(t)=

Solve the initial value problem 9(t+1) dy dt −6y=18t,
9(t+1)dydt−6y=18t, for t>−1 t>−1 with y(0)=14. y(0)=14. Find
the integrating factor, u(t)= u(t)= , and then find y(t)= y(t)=

For 2y' = -tan(t)(y^2-1) find general solution (solve for y(t))
and solve initial value problem y(0) = -1/3

Find y(t) solution of the initial value problem
3ty^2y'-6y^3-4t^2=0, y(1)=1, t>0

For the initial value problem
• Solve the initial value problem.
y' = 1/2−t+2y withy(0)=1

solve the initial value problem y''-2y'+5y=u(t-2) y(0)=0
y'(0)=0

Solve the following initial-value problem by using integrating
factors: ?2y′ + ?? = 1 , x > 0 , y (1) = 2

Use the method of laplace transforms to solve the following
Initial Value Problem:
y"+2y'+y=g(t), y'(0)=0

solve the given initial value problem
dx/dt=7x+y x(0)=1
dt/dt=-6x+2y y(0)=0
the solution is x(t)= and y(t)=

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