Which differential equations are Linear and find their Proper Linear Form

[Northbysouth]

Homework Statement

Which of the following differential equations are linear? Put the linear differential equations in proper linear form

a) t²dy/dt -e^t = ty

b) dy/dt + ytan(t) -e^ty⁽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.

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

Which of the following differential equations are linear? Put the linear differential equations in proper linear form

a) t²dy/dt -e^t = ty

b) dy/dt + ytan(t) -e^ty⁽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.

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?

Homework Equations

The Attempt at a Solution