Free Printable LDE

1.

The general solution of homogeneous LDE with constant coefficients is called as

a)

Complementary Function

b)

Auxiliary Function

c)

Particular integral

2.

$The\ general\ solution\ of\ \frac{\text{d}^2y}{\text{d}x^2}+a^2y=0$

a)

$y\left(x\right)=\ A\ \cos\ ax+B\ \sin ax$

b)

$y\left(x\right)=A\ \cosh\ ax\ +B\ \sinh\ ax$

c)

$y\left(x\right)=\left(Ax+B\right)e^{ax}$

3.

$If\ f\left(D\right)y=e^{ax},f\left(a\right)\ne0,\ then\ P.I.\ is$

a)

$\frac{1}{f\left(a\right)}e^{ax}$

b)

$\frac{1}{f'\left(a\right)}e^{ax}$

c)

$x\frac{1}{f'\left(a\right)}e^{ax}$

4.

$The\ P.I.\ of\ \left(D^2-2D+1\right)y=e^x\ is\$

a)

$\frac{1}{2}e^x$

b)

$\frac{xe^x}{2}$

c)

$\frac{x^2}{2}e^x$

5.

$The\ P.I.\ of\ \left(D^2+a^2\right)y=\sin ax\ is$

a)

$\frac{\left(-x\ \sin\ ax\ \right)}{2}$

b)

$\frac{\left(x\ \sin\ ax\right)}{2}$

c)

$\frac{\left(-x\ \cos\ ax\right)}{2}$

6.

$The\ P.I.\ of\ \left(D^2-a^2\right)y=\cos\ ax\ \ is$

a)

$\frac{\left(x\cos\ ax\right)}{2a^2}$

b)

$\frac{\left(-\ \cos\ ax\right)}{2a^2}$

c)

$\frac{\left(x\sin\ ax\right)}{2a^2}$

7.

$The\ P.I.\ of\ \left(D^2+2\right)y=x^2$

a)

$\frac{\left(x^2+1\right)}{2}$

b)

$\frac{\left(x^2-1\right)}{2}$

c)

$\frac{\left(x+1\right)}{2}$

d)

$\frac{\left(x-1\right)}{2}$

8.

The\ C.F.\ of\ \frac{\text{d}^2x}{\text{d}y^2}+2\frac{\text{d}x}{\text{d}y}+x=\frac{e^{-y}}{y^2}

a)

$\left(C_1+C_2x\right)e^{-x}$

b)

$\left(C_1+C_2y\right)e^{-y}$

c)

$C_1e^y+C_2e^{-y}$

d)

$C_1e^x+C_2e^{-x}$

9.

The\ P.I.\ of\ \frac{\text{d}^2x}{\text{d}y^2}+2\frac{\text{d}x}{\text{d}y}+x=\frac{e^{-y}}{y^2}

a)

$-e^{-x}\log x$

b)

$-e^{-y}\log y$

c)

$e^x\log x$

d)

$e^y\log y$

10.

$The\ general\ solution\ of\ \frac{\text{d}^4x}{\text{d}t^4}-x=0$

a)

$t=ae^{-x}+be^x+c\cos\ x\ +d\ \sin x$

b)

$x=ae^t+be^{-t}+c\ \cos\ t\ +d\ \sin\ t$

c)

$x=\left(a+bt+ct^2+dt^3\right)$

d)

$x=\left(a+bt\right)\cos t+\left(c+dt\right)\sin t$

LDE

Total questions: 10

Worksheet time: 7mins

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