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Find an explicit general solution to the following differential equation,x{y}'=2y + ...

Question:

{eq}Find\, \, an\, \, explicit\,\, general\,\, solution\, \, to\, \, the\,\, following\, \, differential\, \, equation {/eq}

{eq}\mathbf{ x{y}'=2y\, +\, x^{3}cos(x)} {/eq}

Differential Equation:

Equation with derivative term is called differential equation.

Differential equation of form {eq}\displaystyle y'+Py=Q {/eq} is called linear differential equation.

where, P & Q are constant or function of x.

Solution will be

{eq}\displaystyle y\left(I.F\right)=\int \:Q\left(I.F\right)dx+C {/eq} with integrating factor {eq}\displaystyle I.F=e^{\int \:P\:dx} {/eq}

Answer and Explanation: 1

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Given differential equation is

{eq}\displaystyle xy'=2y+x^3cos\left(x\right)\: {/eq}

==> {eq}\displaystyle...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.


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