Differential Equations

Differential Equations

What is a Differential Equation?

Differential Equation

It is an equation involving a function and one or more of its derivatives. If the function has only one independent variable the equation is called an ordinary differential equation.

eg. x(dy/dx)+y=0 

Order 

It is the order of the highest derivative present in the differential equation.

eq. 

Degree

• It is the highest positive integral exponent of the highest order derivative occuring in the differential equation.

• 1) Differential equation must be a polynomial equation in derivative i.e. y',y'' etc

• 2) Derivative must be free from the radicals and fraction.

Multiple Choice

Find the order and degree of the differential equation

 $\frac{dy}{dx}=4x$  

• 1,0

• 0,1

• 1,1

• 0,0

Multiple Choice

 $\frac{d^3y}{dx^{3\ }}+y=0$  

• 1,3

• 3,1

• 1,1

• 3,3

Multiple Choice

 $\left(\frac{d^2y}{dx^2}\right)^{2\ }+\left(\frac{dy}{\left(dx\right)}\right)+2=0$  

• 2,2

• 0,0

• 2,0

• 0,2

Multiple Choice

 $y=x\ \left(\frac{dy}{dx}\right)+\frac{c}{\left(\frac{dy}{dx}\right)}$  

• 2,1

• 1,2

• not defined

• 1,1

Multiple Choice

 $\frac{dy}{dx}+\sin\left(\frac{dy}{dx}\right)=0$  

• 1,not defined

• not defined,1

• 1,1

• both not defined

Multiple Choice

 $\sqrt{\left(\frac{dy}{dx}\right)\ }-4\ \frac{dy}{dx}-7x=0$  

• 2,1

• 1,1/2

• 1/2 ,1

• 1,2

Multiple Choice

 $\alpha=\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}}$  

• 1,1

• 2,2

• not defined

• 2,1

Multiple Choice

 $\frac{d^5y}{dx^5}+\frac{d^2y}{dx^2}+e^{\left(\frac{dy}{dx}\right)}=0$  

• 5,2

• 5,1

• 5,not defined

• 2,5

Multiple Choice

 $y=x\left(\frac{dy}{dx}\right)+\sqrt{\left(a^2\left(\frac{dy}{dx}\right)^2+b^2\right)}$  

• 1,2

• 2,1

• not defined

• 1,1

Multiple Choice

 $\frac{dy}{dx}+\sin\left(\frac{dy}{dx}\right)=0$  

• 1,not defined

• not defined,1

• 1,1

• both not defined