Find the general solution of the first-order linear differential equation.

A)
B)
C)
D)
E)

Question

​Find the general solution of the first-order linear differential equation. ​
​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The given differential equation is of the form y' + 3y = 6. This is a first-order linear differential equation in standard form, where p(x) = 3 and q(x) = 6. The general solution of this differential equation is y(x) = e^(-∫p(x)dx)[∫q(x)e^(∫p(x)dx)dx + C]. Substituting the values of p(x) and q(x), we get y(x) = e^(-3x)[2x + C], where C is the constant of integration. Therefore, the correct answer is option C.

​Find the General Solution of the First-Order Linear Differential Equation

Find the General Solution of the First-Order Linear Differential Equation