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
A differential equation is a mathematical equation that relates an unknown function to its derivatives. It describes the relationship between a function and its rate of change over time or space.
A differential equation is considered linear if the unknown function and its derivatives appear in a linear manner. This means that the function and its derivatives are raised to the first power and are not multiplied or divided by each other.
The proper linear form of a differential equation is when the unknown function and its derivatives are on one side of the equation and all other terms are on the other side. The unknown function and its derivatives should also be raised to the first power and not multiplied or divided by each other.
To solve a linear differential equation, you must first put it in proper linear form. Then, you can use methods such as separation of variables, integrating factors, or substitution to solve for the unknown function.
Yes, some non-linear differential equations can be transformed into linear form through the use of substitution or other methods. However, not all non-linear differential equations can be transformed into linear form.