Question

d^4x/dt^4 + 4x = 0 by differential equations i need a complete solution?​

Answer 1

Answer:

The characteristic equation is

u⁴ + 4 = 0

=> u⁴ = -4

=> u = ± 1 ± i

So the general form of solutions for this differential equation is:

$\displaystyle x = A e^{(1+i)t} + Be^{(1-i)t} + Ce^{(-1+i)t} + De^{(-1-i)t}$

Using the Euler formula $e^{i\theta}=\cos\theta+i\sin\theta$, this can be expressed alternatively as

$\displaystyle x = a\,e^t\cos t+b\,e^t\sin t+c\,e^{-t}\cos t+d\,e^{-t}\sin t$

Answer 2

Answer:

Step-by-step explanation:

Given :

Angles of a quadraliteral are (p + 25)°, 2p°, (2p - 15)° and (p + 20)°

To Find :

The value of largest angle

Solution :

The sum of all four interior angles of a quadraliteral is 360°.

\begin{gathered} \\ : \implies \sf \: (p+25) {}^{ \circ} + 2p {}^{ \circ} + (2p - 15) {}^{ \circ} + (p+20) {}^{ \circ} = {360}^{ \circ} \\ \\ \end{gathered}

:⟹(p+25)

∘

+2p

∘

+(2p−15)

∘

+(p+20)

∘

=360

∘

​

\begin{gathered} \\ : \implies \sf \: 6p + 30 = {360}^{ \circ} \\ \\ \end{gathered}

:⟹6p+30=360

∘

​

\begin{gathered} \\ : \implies \sf \: 6p = 360 - 30 \\ \\ \end{gathered}

:⟹6p=360−30

​

\begin{gathered} \\ : \implies \sf \: 6p = 330 \\ \\ \end{gathered}

:⟹6p=330

​

\begin{gathered} \\ : \implies \sf \: p = \dfrac{330}{6} \\ \\ \end{gathered}

:⟹p=

6

330

​

​

\begin{gathered} \\ : \implies{\underline{\boxed{\pink{\mathfrak{p = 55}}}}} \: \bigstar \\ \\ \end{gathered}

:⟹

p=55

​

​

★

​

Then the values of angles are ,

(p + 25)° = 55 + 25 = 80°

2p° = 55(2) = 110°

(2p - 15)° = 2(55) - 15 = 110 - 15 = 95°

(p + 20)° = 55 + 20 = 75°

Among the given angles of quadrilateral , 110° is largest angle.

Hence ,

The value of largest angle among the given angles of quadrilateral is 110°. So , Option(b) is the required answer