Differential Equations Answers

Solve this Diffrential equation (1-x^2)y"-2xy'+n(n+1)y=0 using Power Series Method

F or the follow ing differential equation locate and classify its singular points on the x-axis

𝑥²𝑦′′+ (2−𝑥)𝑦′= 0.

Find a power series solution of 𝑥𝑦′=𝑦

1) dx/dy+4y=12 for y(0)=1 (general nad particular solution)

Find the solution of (3x-y+6)dx +(6x-2y-6)dy=0 using Case 1

Many scientists believe that large asteroid struck the earth that kill off dinosaurs. Fragment of asteroid had found out and contain 86% of its original uranium-238. How old is the fragment of the asteroid? The half-life of uranium-238 is 4.5 billion years

Find the equation of the curve at every point that passes through the point (0, −1) and which the normal line at any point (x, y) has a slope of 1/(3x + 2).

The particular integral of (D³ - 2D²D')z = sin (x + 2y) is

Solve the following Bernoulli's Differential Equations. Show your solutions.

a. dy/dx + (1/3) y = e^x y²

b. x (dy/dx) + y = xy³

c. dy/dx + (2/x) y = -x² cos x y²

d. x²y-x³ (dy/dx) = y² cos x

Solve this Diffrential equation (1-x^2)y"-2xy'+n(n+1)y=0 using Power Series Method