Higher order linear differential equations

The complete solution(or complete integral ) of Linear Differential equations involves

• complete function + particular integral

• complementary function + particular integral

• complementary function + definite integral

• complete function + indefinite integral

The particular integral of the equation  $\left(D-1\right)y=e^{3x}$  is

•  $\frac{e^{3x}}{2}$  

•  $\frac{e^{-3x}}{2}$  

•  $\frac{e^{3x}}{4}$  

•  $\frac{e^x}{2}$  

The C.F. of the equation  $\left(D^2-9\right)y=e^{-3x}+1+e^{3x}$  is

•  $c_1e^{-3x}+c_2e^{-x}$  

•  $c_1e^{3x}+c_2e^{3x}$  

•  $c_1e^{3x}+c_2e^{-x}$  

•  $c_1e^{3x}+c_2e^{-3x}$  

Number of arbitrary constant in the general solution of a differential equation of degree 3 and order 4 is

• 3

• 4

• 0

• 4³

 $\frac{\text{d}^2x}{\text{d}y^2}+6\frac{\text{d}x}{\text{d}y}-5y=0\$  

The general solution to the DE is,

•  $y=Ae^x+Be^{5x}$  

•  $y=Ae^{-x}+Be^{-5x}$  

•  $y=Ae^{\left(-3+\sqrt{14}\right)x}+Be^{\left(-3-\sqrt{14}\right)x}$  

•  $y=A\cos\left(-3+\sqrt{14}\right)x+B\sin\left(-3-\sqrt{14}\right)x$  

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$  

• Separable.

• Non Separable

Differential equation of the curve y= Acos2x+B sin2x , where A & B are constant is

• y^"+4y=0

• y^"-4y=0

• y^" -4y^'=0

• y^"+4y^'=0

The complementary function of the equation  $2\frac{d^2y}{dt^2}+5\frac{\text{d}y}{\text{d}t}-12y=0$  is

•  $c_1e^{\frac{3}{2}x}+c_2e^{-4x}$  

•  $c_1e^{\frac{3}{2}t}+c_2e^{-4t}$  

•  $c_1e^{-\frac{3}{2}x}+c_2e^{4x}$  

•  $c_1e^{-\frac{3}{2}t}+c_2e^{4t}$  

The particular integral of the equation   $\left(D^3-1\right)y=\left(e^x+1\right)^2$  is

•  $\frac{e^{-2x}}{7}+\frac{2x}{3}-1$  

•  $\frac{e^{3x}}{7}+\frac{2x}{3}-1$  

•  $\frac{e^{2x}}{7}+\frac{5x}{3}-1$  

•  $\frac{e^{2x}}{7}+\frac{2x}{3}-1$  

The P.I. of the equation  $\left(D^3+D\right)y=\cos x\$  is

•  $-\frac{x\cos x}{2}$  

•  $\frac{x\cos x}{2}$  

•  $-\frac{\cos x}{2}$  

•  $-\frac{x\cos x}{5}$