Chapter 14, Second Order Linear Differential Equations Video Solutions, Engineering Mathematics Through Applications

Problem 1

Determine the displacement $s$ in each of the following cases:
a $\frac{\mathrm{d}^{2} s}{\mathrm{~d} t^{2}}=-9.8$ given that at $t=0$, both $\frac{\mathrm{d} s}{\mathrm{~d} t}=0$ and $s=0$
b $\frac{\mathrm{d}^{2} s}{\mathrm{~d} t^{2}}=9.8 t$ given that at $t=0$, both $\frac{\mathrm{d} s}{\mathrm{~d} t}=0$ and $s=0$
c $\frac{\mathrm{d}^{2} s}{\mathrm{~d} t^{2}}=a(a$ is acceleration) given that at $t=0$, both $\frac{\mathrm{d} s}{\mathrm{~d} t}=u$ and $s=0$

Manisha Sarker

Numerade Educator

03:31

Problem 2

Find the general solutions of the following equations:
$\mathbf{a} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+5 \frac{\mathrm{d} y}{\mathrm{~d} x}+6 y=0$
$\mathbf{b} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+4 \frac{\mathrm{d} y}{\mathrm{~d} x}+4 y=0$
$\mathbf{c} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-2 \frac{\mathrm{d} y}{\mathrm{~d} x}+4 y=0$

Charles Machakwa

Numerade Educator

06:39

Problem 3

Solve:
$\mathbf{a} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+3 \frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=0$
$\mathbf{b} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-7 \frac{\mathrm{d} y}{\mathrm{~d} x}+6 y=0$
$\mathbf{c} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-6 \frac{\mathrm{d} y}{\mathrm{~d} x}+9 y=0$
d $\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-4 \frac{\mathrm{d} y}{\mathrm{~d} x}+5 y=0$
e $\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-8 \frac{\mathrm{d} y}{\mathrm{~d} x}+16 y=0$

Wasim Sher

Numerade Educator

03:05

Problem 4

Solve:
$\mathbf{a} \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+6 \frac{\mathrm{d} y}{\mathrm{~d} x}+9 y=0$
b $10 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+50 \frac{\mathrm{d} y}{\mathrm{~d} x}+250 y=0$
$\mathbf{c}-\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-3 \frac{\mathrm{d} y}{\mathrm{~d} x}+8 y=0$

M Hassan Anwar

Numerade Educator