Question

Solve the following ODE's/ IVP's

y'=1/xsin(y)+2sin(2y)

Hint: consider x=x(y) and dx/dy=1/(dx/dy)=1/y'

Answer #1

(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 following DE:
x dy/dx + 2y = x^2 - x + 1 ; y(1) = 1/2

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

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

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

Solve the initial value problems.
1) x (dy/dx)+ 2y = −sinx/x , y(π) = 0.
2) 3y”−y=0 , y(0)=0,y’(0)=1.Use the power series method
for this one . And then solve it using the characteristic
method
Note that 3y” refers to it being second order
differential and y’ first

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

SOLVING SYSTEMS OF LINEAR DEs BY ELIMINATION
Solve
Dx=y-1
Dy =2y-3x

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

Solve: 1.dy/dx=(e^(y-x)).secy.(1+x^2),y(0)=0.
2.dy/dx=(1-x-y)/(x+y),y(0)=2 .

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 16 minutes ago

asked 35 minutes ago

asked 42 minutes ago

asked 44 minutes ago

asked 53 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago