Math 251, Exam 1 Review
Differential Equation (ex?)
An equation that contains one or greater derivatives of an unknown characteristic (sample
exs: y'' - 3y' + 5y = t^2 or y''(t^2 • y') = (ye^(5t))/t
Ordinary Differential Equation
A differential equation concerning a function of most effective 1 variable
Partial Differential Equation
A differential equation concerning a feature of 2 or greater variables AND their partial
derivatives (pattern ex in photo)
Order
The highest derivative taken in a differential equation (note: NOT powers)
Linear Differential Equation
A differential equation in which the based variable (or "y" in the case of "dy/dx")
Constant answers
Also referred to as equilibrium answers or stationary factors. First order functions become
regular numbers, and for this reason, their derivatives emerge as zeros. A "solution" is the
result after the simplification
What makes an equation "separable"?
The equation is separable if it may be written inside the shape [ M(x) + N(y)y' = 0 ], in which
m(x) includes handiest x's and N(y) includes handiest y's. It lets in the x's and y's to be
separated to extraordinary sides of the equation
What are the steps to solving a separable differential equation?
1. Rearrange the equation so all variables are on their personal side
2. Integrate both facets with recognize to their variables, remembering the steady on one
side
3. Solve for C, commonly with preliminary conditions
4. Try to find an explicit answer if feasible
Differential Equation (ex?)
An equation that contains one or greater derivatives of an unknown characteristic (sample
exs: y'' - 3y' + 5y = t^2 or y''(t^2 • y') = (ye^(5t))/t
Ordinary Differential Equation
A differential equation concerning a function of most effective 1 variable
Partial Differential Equation
A differential equation concerning a feature of 2 or greater variables AND their partial
derivatives (pattern ex in photo)
Order
The highest derivative taken in a differential equation (note: NOT powers)
Linear Differential Equation
A differential equation in which the based variable (or "y" in the case of "dy/dx")
Constant answers
Also referred to as equilibrium answers or stationary factors. First order functions become
regular numbers, and for this reason, their derivatives emerge as zeros. A "solution" is the
result after the simplification
What makes an equation "separable"?
The equation is separable if it may be written inside the shape [ M(x) + N(y)y' = 0 ], in which
m(x) includes handiest x's and N(y) includes handiest y's. It lets in the x's and y's to be
separated to extraordinary sides of the equation
What are the steps to solving a separable differential equation?
1. Rearrange the equation so all variables are on their personal side
2. Integrate both facets with recognize to their variables, remembering the steady on one
side
3. Solve for C, commonly with preliminary conditions
4. Try to find an explicit answer if feasible
