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

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,

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


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


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

Basic Cal.

Hi! I need help with these.


Help a Calculus dummy.

How do I solve these? Help po.

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.


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 = p0 at the inner wall r = r1 and is negligible (p = 0) at the outer wall r = r2 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.

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