# Calculus

## A Beginner's Guide to Differentiation and Integration: Unlocking the Power of Calculus

Introduction:

Welcome to the Beginner's Guide to Differentiation and Integration, where we'll explore the fundamental concepts of calculus that form the backbone of mathematical analysis. Whether you're a student just starting to delve into calculus or someone looking to refresh their understanding, this guide will provide you with a solid foundation in differentiation and integration. So, let's embark on this exciting journey into the world of calculus!

## Differential Equation: $(1-xy)^{-2} dx + \left[ y^2 + x^2 (1-xy)^{-2} \right] dy = 0$

Hello, can anyone solve this equation?

I can't figure it out,

$(1-xy)^{-2} dx + \left[ y^2 + x^2 (1-xy)^{-2} \right] dy = 0$

Thanks.

## Differential Equation: $y' = x^3 - 2xy$, where $y(1)=1$ and $y' = 2(2x-y)$ that passes through (0,1)

Can anyone solve this D. E.?

y' = x^3 - 2xy, where y(1)=1

and

y' = 2(2x-y) that passes through (0,1)

## Basic Cal.

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## Basic Calculus

Help me find the limits of these:

Help me identify all asymptotes and the end behavior of the graph:

## Families of Curves: family of circles with center on the line y= -x and passing through the origin

**Find the diff equation of family of circles with center on the line y= -x and passing through the origin.**

THANK YOU :)

## Applications Of Differential Equations

The radial stress *p* at distance r for the axis of the thick cylinder subjected to internal pressure is given by p + r (dp/dr) = A − p where *A* is a constant. If p = p_{0} at the inner wall r = r_{1} and is negligible (p = 0) at the outer wall r = r_{2} find an expression for p.

## Eliminating arbitrary constants

kindly help me with my homework. eliminate the following arbitrary constants...

y= x^2 + c1 e^3x + c2 e^3x.