Partial Differential Equations Exam Questions with Correct Answers

Partial Differential Equations Exam Questions with Correct Answers What is the order of a differential equation? - Answer-The order of a DE is the order of the highest derivative that appears in the equation What is the degree of the differential equation? - Answer-The degree of the DE is the power of the highest derivative involved When is a differential equation linear? - Answer-A DE is linear if the function F, such that F(x,t,y(x,t)),dy/dx(x,t),dy/dt(x,t),...) is a linear function of y and its derivatives What is cosh(x) and sinh(x) in terms of the exponential function? - Answer-cosh(x) = (e^x + e^-x)/2 sinh(x) = (e^x - e^-x)/2 What are the different types/methods of solving first order ODEs ? (5)` - Answer-(1) Direct Integration (2) Seperable Variables (3) Homogeneous 1st-order ODE (4) Linear 1st-order ODE (5) Exact 1st-order ODE What is the form of a homogeneous 1st-order ODE? How do we solve them? - Answer-dy/dx = g(y/x) for some function g. We can solve by the change of variables z = (y/x) (SEE NOTES FOR MORE) What is the form of a linear 1st-order ODE? How do we solve them? - Answer-(dy/dx) + p(x)y = r(x)