Question

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

Answer #1

Use the method for solving Bernoulli equations to solve the
following differential equation
dx/dy+5t^7x^9+x/t=0
in the form F(t,x)=c

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

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

Solve the given differential equation by using an appropriate
substitution. The DE is of the form dy dx = f(Ax + By + C), which
is given in (5) of Section 2.5. dy/dx = (x + y + 7)^2

Homogenous Differential Equations:
dy/dx = y - 4x / x-y
dy/dx = - (4x +3y / 2x+y)

Solve the following system of differential equations:
dx/dt =x+2y
dy/dt =−x+3y

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

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

Find the solution for the differential equation
( 4tan(4x) − 4sin(4x) sin(y) ) dx + ( cos(4x) cos(y) ) dy = 0
Has solutions of form F( x, y ) = c ,where
F ( x ,y ) = ?
Please show your work step by step, thanks.

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

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