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


{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

Become a member to unlock this answer! Create your account

View this answer

Given differential equation is

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

==> {eq}\displaystyle...

See full answer below.

Learn more about this topic:

First-Order Linear Differential Equations


Chapter 16 / Lesson 3

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.

Related to this Question

Explore our homework questions and answers library