Differential Equations 2024 Test with Complete Solutions

Differential Equations 2024 Test with Complete Solutions Differential Equation - Answer-Is an equation with a function and one or more of it's derivatives. The Order of the equation - Answer-Is the highest derivative occurring in the equation. First Order DE - Answer-Is one containing a first--but no higher--derivative of the unknown function. " F(x) = ..." - Answer-A classic way of writing a function Function - Answer-Is like a machine that has an input and an output What is a function? - Answer-It relates the input to an output F(x,y) - Answer-A function of two variables, x and y. When can I use the "separation of variables" method? - Answer-When all the y terms (including dy) can be moved to one side of the equation, and the x terms can be moved to the other side of the equation. Separation of Variables - Answer-Is a special method to solve some differential equations In mathematics, a homogeneous function - Answer-is one with multiplicative scaling behavior: if all it's arguments are multiplied by a factor (t) , then its value is multiplied by some power(^n) of this factor. dy/dx = xsinx | ysinx | xsiny | xsiny + ysinx - Answer-FIRST ORDER differential equation d^2y/dx^2 = -1/100 (dy/dx) - k(y - (1/6)y^3)) - Answer-SECOND ORDER differential equation dy/dx = xsinx | ysinx | xsiny - Answer-SEPARABLE differential equations, since they can be rewritten as [ dxf(x) = dyg(y) ] for appropriate f and g.