(1 pt) It can be helpful to classify a differential equation, so that we can pre
ID: 2967909 • Letter: #
Question
(1 pt) It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Three classifications are the order of the equation - (what is the highest number of derivatives involved), whether or not the equation is linear, and whether the equation is homogeneous or non-homogeneous Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: 1. t^2 d^2y/dt^2 + t dy/dt + 2y = sin t 2. d^4y/dt^4 + d^3y/dt^3 + d^2y/dt^2 + dy/dt = 1 3. d^3y/dt^3 + t dy/dt + (cos^2(t))y = t^3 4. y'' - y + t^2 = 0Explanation / Answer
1. t2(d2y/dt2)+t(dy/dt)+2y=sin t
Answer:- 2nd. order linear nonhomogeneous differential equation
2. forth order nonhomogeneous differential equation
3.(d3y/dt3)+t(dy/dt)+(cos2(t))y=t3
Answer:- 3rd. order linear homogeneous differential equation
y''-y+t2=0
g. 2nd. order linear homogeneous differential equation
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.