Question

solve these differential equations and state the equilibrium solutions if any exist.

y'= x^2 +2x + 1

f'(x)=e^x +1

y'= sinx + x

Answer #1

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Solve the given system of differential equations by
elimination.
x'-2x-y = 1
x+y'-4y=0

Solve the differential equations
(2D^2 + D - 3)y = 2x - 3x^2

Find all solutions to the differential equations.
(a) x^2 yy' = (y^2 − 1)^(3/2)
(b) y' = 6xe^(x−y)
(c) y' = (2x − 1)(y + 1)
(d) (y^2 − 1) dy/dx = 4xy^2
Leave your answer as an implicit solution

Given use Laplace transform to solve the following systems of
differential equations.
2x' - y' - z' = 0
x' + y' = 4t + 2
y' + z = t2 + 2
SUBJECT = ORDINARY DIFFERENTIAL EQUATIONS
TOPIC = LAPLACE TRANSFORM

solve the following differential equations or initial value
problems answers may be left as implicit solutions (or in terms of
an integral).
y'=5y+e^(-2x)y^(-2) y(0)=2

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

solve the given DE equation y''-4y'+20y= (x+1)e^2x cos x + 2x^2
e^2x sinx

Use the method for solving Bernoulli equations to solve the
following differential equation.
(dy/dx)+4y=( (e^(x))*(y^(-2)) )
Ignoring lost solutions, if any, the general solution y=
______(answer)__________
(Type an expression using x as the variable)
THIS PROBLEM IS A DIFFERENTIAL EQUATIONS PROBLEM. Only people
proficient in differential equations should attempt to solve.
Please write clearly and legibly. I must be able to CLEARLY read
your solution and final answer. CIRCLE YOUR FINAL ANSWER.

1- Solve Ordinary Differential Equations
A) (xˆ2 + 1) y '+ 4xy = x
B) y '+ ((2x + 1) / x) y = exp (-2x)
C) y '+ y = sen (x)
D) y'-2xy = x

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