Question

solve the differential equation

(2y^2+2y+4x^2)dx+(2xy+x)dy=0

Answer #1

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

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

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

Solve the Differential Equation:
(2y^4 + xy)dx - (6x^2) dy= 0

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

Solve the first order homogeneous differential equation:
(2x-5y)dx + (4x-y) dy=0

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

(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=

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

Use the method for solving equations of the form
dy/dx=G(ax+by)
to solve the following differential equation.
dy/dx=2sin(4x-2y) ignore lost solutions and give implicit
solution in the form F(x,y)=c

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