Question

Solve each of the following equations. Implicit answers are acceptable.

a.) y'-y= cos(x)

with no initial conditions and:

b.) y'= e^{(x)}y^{-1}

with initial conditions y(0)=0

Answer #1

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 system of differential equations using Laplace
transform:
y'' + x + y = 0
x' + y' = 0
with initial conditions
y'(0) = 0
y(0) = 0
x(0) = 1

1. Solve the following IVP's given the initial conditions:
a) y'(t) - 10(√t)y(t) =
e(20/3)(t^3/2) ; y(0) = 2
b) x' - 2x = (et)(cos(t)) ; x(0) = 5
c) dx/dt + (1/t)x = ln(t) ; x(1) = 1/2

How many solutions of the equation y^(3) = x + cos(x) satisfy
the following initial conditions: y(0) = y ′ (0) = y^((2))(0) =
0.5

Solve the Initial Value Problem
(y2 cos(x) − 3x2y − 2x) dx + (2y sin(x) −
x3 + ln(y)) dy = 0, y(0) = e

Solve the following differential equations with initial
conditions:
xy'-y=3xy1/2

solve the initial value problem
y''+8y=cos(3t), y(0)=1, y'(0)=-1

Solve the following system of equations simultaneously. Give
answers for both x and y.
2x-5y=1
x+3y=6

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 following differential equations through order
reduction.
(a) xy′y′′−3ln(x)((y′)2−1)=0.
(b) y′′−2ln(1−x)y′=x.

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