Ordinary differential equations

A differential equation in which the function depends on only one independent variable is called a ................

• partial differential equation

• linear equation

• ordinary differential equation

• non linear equation

A differential equation in which the function depends on more than one independent variabls is called a ................

• partial differential equation

• linear equation

• ordinary differential equation

• non linear equation

The general solution of the ODE contains .........

• complementary function only

• particular integral only

• both complementary function and particular integral

• neither complementary function nor particular integral

The complementary function is the solution of .........

• homogeneous ordinary differential equation

• linear equation

• non linear equation

• partial differential equation

 The auxiliary equation of the following ODE 
 $\left(D^2-3D+5\right)y=0$ is..............

•  $m^2-3m+5=0$  

•  $m^2+3m-5=0$  

•  $m^2-3m+5$  

•  $\left(m^2-3m+5\right)y=0$  

 The auxiliary equation of the following ODE 
 $D^2y-7Dy+6y=0$ is..............

•  $m^2-7m+6=0$  

•  $m^2+7m-6=0$  

•  $m^2-3m+5$  

•  $\left(m^2-7m+6\right)y=0$  

 The roots of the auxiliary equation
 $m^2-7m+12=0$ 

are.....................

• -3, -4

• 3,  -4

• 3 ,4

• -3, 4

If the roots of the auxiliary equation in an ODE are 5 and 6, then complementary function is y=.......................

•  $Ae^{5x}+Be^{6x}$  

•  $Ae^{-5x}+Be^{-6x}$  

•  $Ae^{5x}+xBe^{6x}$  

If the roots of the auxiliary equation in an ODE are 5 and 5, then complementary function is y=.......................

•  $Ae^{5x}+xBe^{5x}$  

•  $Ae^{-5x}+xBe^{-5x}$  

•  $Ae^{5x}+xBe^{6x}$  

If the roots of the auxiliary equation in an ODE are 1, -1, i, -i, then complementary function is y=.......................

•  $Ae^x+Be^{-x}+C\cos x+D\sin x$  

•  $Ae^x+Be^{-x}+C\cos x-D\sin x$  

•  $Ae^x+xBe^{-x}+C\cos x+D\sin x$   

•  $Ae^{ix}+Be^{-ix}+C\cos x+D\sin x$