Linear equation and linear differential equationsI remember noting from an algebra class that x and y of a linear equation neither divide or multiply with each other which is somewhat clear from the forms of linear equations:General form of linear equation: A x + B y + C = 0Slope intercept form: y = m x + bIs this also true for linear differential equations?The definition goes like this: "A differential equation is said to be linear if the dependent variable and its differential coeficients (derivates) occur only in the first degree and not multiplied together." d y d x = P y + Q Where P, Q are functions of x only. What exactly does this mean?Does the algebraic linear equation has something to do with linear differential equation?

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Linear equation and linear differential equationsI remember noting from an algebra class that x and y of a linear equation neither divide or multiply with each other which is somewhat clear from the forms of linear equations:General form of linear equation:  A  x  +  B  y  +  C  =  0Slope intercept form:  y  =  m  x  +  bIs this also true for linear differential equations?The definition goes like this: &quot;A differential equation is said to be linear if the dependent variable and its differential coeficients (derivates) occur only in the first degree and not multiplied together.&quot;                    d        y                    d        x              =      P    y    +    Q  Where P, Q are functions of x only. What exactly does this mean?Does the algebraic linear equation has something to do with linear differential equation?

acorazarxf · Accepted Answer

Step 1It&#039;s saying that if x and y (or their derivatives) are multiplied together in any way, it&#039;s not considered a linear differential equation because it&#039;s not solvable in the usual ways that linear ODE&#039;s are.Step 2This relates to normal linear equations in that if you have an equation where x and y are multiplied or otherwise modify each other in a way that prevents strict separation in the polynomial, they do not have a linear relationship. For example, the plot of   y  =  1      /    x is not a line while   y  =  x is.

Linear equation and linear differential equations. General form of linear equation: Ax+By+C=0. Slope intercept form: y=mx+b. Is this also true for linear differential equations?

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