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Solve the differential equation.$ y' + 2xy = 1 $

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$$y=\frac{\int e^{x^{2}} d x}{e^{x^{2}}}$$

01:17

Amrita Bhasin

Calculus 2 / BC

Chapter 9

Differential Equations

Section 5

Linear Equations

Ebru U.

December 21, 2021

Solve y”-4y’+5y=8e^2x+2e^2x*cosx can someone solution this question to step by step please?

Solve y”-2y’+y=e^x*lnx when x>1

Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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Solve the differential equ…

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Solve the given differenti…

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okay. We wanna solve this differential equation. So first, make sure why Prime is by itself. It is now find the integrating factor. And the integrating factor is e to the integral of what's ever in front of why two x dx. So that's each the X squared. So multiply everything by that. All right, I claim that this side is eat the X squared. Why? Quantity prime? Let's check and see. It's the first each the X squared times the derivative of the second. Why prime Plus the second Why times the derivative of the first, which is easy to the export times two x. All right now I'm gonna integrate both sides on this side. I get each the X squared y on this side. I get the inner girl, eat the X square DX plus c. Okay, that's not an integral that I know. In fact, it can't be integrated. Okay, you have to use some kind of trapezoid rule or something on it to integrate it. So divide each of the X squared on both sides and there is Thea answer to that one

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