Answer:
1. g. 2nd. order non-linear differential equation
2. a. 1st. order linear differential equation
3. c. 3rd. order linear differential equation
4. g. 2nd. order non-linear differential equation
Step-by-step explanation:
QUESTION 1
[tex](1+y^2)(\frac{d^2y}{dt^2})+t\frac{dy}{dt} +y=e^t[/tex]
Order: The highest derivative present in this differential equation is the second derivative ([tex]\frac{d^2y}{dt^2}[/tex]). Hence the order of this differential equation is 2.
Linearity: There is the presence of the product of the dependent variable , [tex]y[/tex] and its derivative [tex][(1+y^2)(\frac{d^2y}{dt^2})][/tex].
Hence this differential equation is non-linear.
Classification: Second order non-linear ordinary differential equation.
QUESTION 2
The given differential equation is
[tex]t^2\frac{d^2y}{dt^2}+t\frac{dy}{dt} +2y=\sin t[/tex]
Order: The highest derivative present in this differential equation is [tex]\frac{d^2y}{dt^2}[/tex]
Hence it is a second order differential equation.
Linearity: There is no presence of the product of the dependent variable and/or its derivative. There is no presence of higher powers of the dependent variable or its derivative. There is no transcendental function of the dependent variable.
Classification: First order linear differential equation
QUESTION 3
The given differential equation is
[tex]\frac{d^3y}{dt^3}+t\frac{dy}{dx} +\cos (2t)y=t^3[/tex]
Order: The highest derivative present in this differential equation is [tex]\frac{d^3y}{dt^3}[/tex]
Hence it is a third order differential equation.
Linearity: There is no presence of the product of the dependent variable and/or its derivative. There is no presence of higher powers of the dependent variable or its derivative. There is no transcendental function of the dependent variable.
Classification: Third order linear ordinary differential equation
QUESTION 4
The given differential equation is;
[tex]y"-y+y^2=0[/tex]
Order: The highest derivative present in this differential equation is [tex]y"[/tex]
Hence it is a second order differential equation.
Linearity: There is the presence of higher power of the dependent variable, [tex]y^2[/tex]. Hence the differential equation is non-linear.
Classification: Second order non-linear differential equation
