Question

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy = 0. (a) Verify this is an exact equation

(b) Solve the equation

Answer #1

solve the differential equation
(2y^2+2y+4x^2)dx+(2xy+x)dy=0

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

(2xy+x^2+3y^2)dy/dx+(y^2+2xy+3x^2)=0

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

consider the equation y*dx+(x^2y-x)dy=0. show that the equation
is not exact. find an integrating factor o the equation in the form
u=u(x). find the general solution of the equation.

(x+1)y'=y-1 2) dx+(x/y+(e)?)dy=0 3)ty'+2y=sint 4) y"-4y=-3x²e3x
5) y"-y-2y=1/sinx 6)2x2y"+xy'-2y=0 ea)y=x' b) x=0
2dx/dt-2dy/dt-3x=t; 2

Solve the equation.
(3 + 3y2 + 3y3) dx + (2xy +
3xy2)dy = 0
An implicit solution in the form F(x,y) = C.

(1 point)
In this problem we consider an equation in differential form
Mdx+Ndy=0Mdx+Ndy=0.The equation
(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0
in differential form M˜dx+N˜dy=0M~dx+N~dy=0 is not exact.
Indeed, we have
M˜y−N˜x=

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).

dx
dt
= y − 1
dy
dt
= −3x + 2y
x(0) = 0, y(0) = 0

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 27 minutes ago

asked 27 minutes ago

asked 47 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago