Essential Partial Differential Equations (2015) –
Solutions Manual – by Griffiths
What is the goal of a differential equation? - answer-To find a function that when substituted
into the differential equation make it true.
What does it mean when a differential equation has an infinite family of solutions? - answer-It
means that the solution of the differential equation contains at least one arbitrary constant.
What is a unique/particular solution of a differential equation? - answer-A solution that is
obtained through the use of an initial condition. That initial condition is used to find the value of
the arbitrary constant
What is linearity? - answer-Linearity is when you add general solutions which increases the
number of arbitrary constants.
How do you check an implicit solution? - answer-You do implicit differentiation!
What is an ordinary differential equation (ODE)? - answer-A differential equation that contains
derivatives with respect to only 1 independent variable.
What is the order of the differential equation? - answer-The highest order derivative that
appears in that equation.
What is a homogenous solution? - answer-g(x) = 0
1
, What is a non homogenous solution? - answer-g(x) not equal to 0
What is a singular solution? - answer-A solution that does not fit the general solution
What is a trivial solution? - answer-y(x) = 0
What is a directly integrable solution? - answer-A directly integrable solution is when a
derivative equals a function of the independent variable, allowing for direct integration to find
the solution.
What is the antiderivative of acceleration? - answer-Velocity
What is the antiderivative of velocity? - answer-Position
How do we find initial velocity? - answer-Initial velocity V₀ = V(0) when t = 0
How do we find initial position? - answer-Initial position X₀ = X(0) when t = 0
What is the first derivative of x(t) or position - answer-x'(t) = velocity v(t)
What is the first derivative of v(t) or velocity - answer-v'(t) = acceleration a(t)
Constant acceleration function - answer-x(t) = at²/2 + v₀t + x₀
falling objects acceleration (meters and feet) - answer-g = -9.8 m/s² = -32 ft/s²
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Solutions Manual – by Griffiths
What is the goal of a differential equation? - answer-To find a function that when substituted
into the differential equation make it true.
What does it mean when a differential equation has an infinite family of solutions? - answer-It
means that the solution of the differential equation contains at least one arbitrary constant.
What is a unique/particular solution of a differential equation? - answer-A solution that is
obtained through the use of an initial condition. That initial condition is used to find the value of
the arbitrary constant
What is linearity? - answer-Linearity is when you add general solutions which increases the
number of arbitrary constants.
How do you check an implicit solution? - answer-You do implicit differentiation!
What is an ordinary differential equation (ODE)? - answer-A differential equation that contains
derivatives with respect to only 1 independent variable.
What is the order of the differential equation? - answer-The highest order derivative that
appears in that equation.
What is a homogenous solution? - answer-g(x) = 0
1
, What is a non homogenous solution? - answer-g(x) not equal to 0
What is a singular solution? - answer-A solution that does not fit the general solution
What is a trivial solution? - answer-y(x) = 0
What is a directly integrable solution? - answer-A directly integrable solution is when a
derivative equals a function of the independent variable, allowing for direct integration to find
the solution.
What is the antiderivative of acceleration? - answer-Velocity
What is the antiderivative of velocity? - answer-Position
How do we find initial velocity? - answer-Initial velocity V₀ = V(0) when t = 0
How do we find initial position? - answer-Initial position X₀ = X(0) when t = 0
What is the first derivative of x(t) or position - answer-x'(t) = velocity v(t)
What is the first derivative of v(t) or velocity - answer-v'(t) = acceleration a(t)
Constant acceleration function - answer-x(t) = at²/2 + v₀t + x₀
falling objects acceleration (meters and feet) - answer-g = -9.8 m/s² = -32 ft/s²
2
