Question

Check if the following functions satisfy the differential equation dy/dx = x+y.

In each case, after your work is complete say whether the function fits the equation.

a. y= -x-1

b. y= e^x -x

c. y=2e^x-x-1

Answer #1

) Check that each of the following functions solves the
corresponding differential equation, by computing both the
left-hand side and right-hand side of the differential
equation.
(a) y = cos2 (x) solves dy/dx = −2 sin(x) √y
(b) y = 4x + 1/x solves x dy dx + 2/x = y
(c) y = e x 2+3 solves dy/dx = 2xy
(d) y = ln(1 + x 2 ) solves e y dy dx = 2x

Solve the given differential equation
y-x(dy/dx)=3-2x2(dy/dx)

(x-y)dx + (y+x)dy =0 Solve the differential equation

Consider the following differential equation: dy/dx =
−(3xy+y^2)/x^2+xy
(a) Rewrite this equation into the form M(x, y)dx + N(x, y)dy =
0. Determine if this equation is exact;
(b) Multiply x on both sides of the equation, is the new
equation exact?
(c) Solve the equation based on Part (a) and Part (b).

Solve the differential equation:
dy/dx = sin(x - y).

Solve the differential equation: dy/dx - y =e^x*y^2 (Using
u=y^-1)

1. Sketch the direction field for the following differential
equation dy dx = y − x. You may use maple and attach your graph.
Also sketch the solution curves with initial conditions y(0) = −1
and y(0) = 1.

Consider the differential equation
x2 dy + y ( x + y) dx = 0 with the initial condition
y(1) = 1.
(2a) Determine the type of the differential equation. Explain
why?
(2b) Find the particular solution of the initial value problem.

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

4) Solve the following differential equation dy dx = y x + x
pls show me the steps

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