The discussion focuses on identifying linear differential equations and converting them into proper linear form. The equations presented are: a) t²(dy/dt) - e^t = ty and b) dy/dt + ytan(t) - e^ty² = 0. The key takeaway is that to determine linearity, all terms involving the dependent variable y and its derivative dy/dt must be isolated on one side of the equation. For equation a), the goal is to express dy/dt explicitly, while for equation b), the presence of y² indicates it is non-linear.
PREREQUISITESStudents studying differential equations, educators teaching calculus, and anyone seeking to improve their algebraic manipulation skills in the context of differential equations.
How does your book define the term, linear differential equation? To get to that form, you don't want to solve for y - you want to put all the terms involving y and y' on one side, and everything else on the other. For a), you would want the left side of the equation to start with dy/dt. What can you do to get dy/dt by itself?Northbysouth said:Homework Statement
Which of the following differential equations are linear? Put the linear differential equations in proper linear form
a) t2dy/dt -et = ty
b) dy/dt + ytan(t) -ety(2)=0
Essentially, I'm struggling with basic algebra. I've had no luck moving the dependent variable, y, to one side and the independent variable,t, to the other. Any suggestions would be appreciated.
Northbysouth said:Homework Equations
The Attempt at a Solution