A tank contains 480 gallons of water in which 60 lbs of salt are dissolved. A sa

Question

A tank contains 480 gallons of water in which 60 lbs of salt are dissolved. A saline solution containing 0.5 lbs of salt is pumped into the tank a, the rate of 2 gallons per minute. The well-mixed solution is pumped out at the rate of 4 gallons per minute. Set up an initial value problem which can be solved for the amount A of salt in the tank at time t. Consider the following differential equation: sin x d^3y/dx^3 - x^2 dy/dx + y In x (a) Is the equation linear or nonlinear? (b) Is it a partial or ordinary differential equation? (c) What is the order of the equation?

Explanation / Answer

6) sin x y'''-x^2 y''+y=ln x can be written as

f(x)y'''-g(x)y''+y=p(x) where f(x)=sin x,g(x)=x^2,p(x)=ln x

the dependent variable and its derivatives are appearing only in first degree and not multiplied together(ie y,y',y'',y''' are independent).So this is a linear differential equation(not partial)

order of equation is highest degree present in the eqation,here it is 3(y''')

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.