Question

Find the series solution of the following equation: (d^2y/dx^20 - x(dy/dx) + ny=0. Where n=0,1,2.

Answer #1

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.

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

Find a general solution: (dy/dx) = (x+xy^2)/2y

find the particular solution for the following initial value
problems
A) x dy/dx +2y = x to the power of 2 +x , y(1)=1

Question 11:
What is the general solution of the following homogeneous
second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a)
y = e 12.5.x (Ax + B)
(b)
y = e -5.x (Ax + B)
(c)
y = e -10.x (Ax + B)
(d)
y = e +5.x (Ax + B)
Question 12:
What is the general solution of the following homogeneous
second-order differential equation?
Non-integers are expressed to one decimal place.
d^2y/dx^2 − 38.y =0
(a)
y...

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 differential equation dy/dx= 2y(x+1)
a) sketch a slope field
b) Show that any point with initial condition x = –1 in the 2nd
quadrant creates a
relative minimum for its particular solution.
c)Find the particular solution y=f(x)) to the given differential
equation with
initial condition f(0) = 2
d)For the solution in part c), find lim x aproaches 0
f(x)-2/tan(x^2+2x)

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

Find the derivatives dy/dx and d^2y/dx^2, and evaluate them at t
= 2.
x=t^2 ,y = t ln t

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