CameraIcon

SearchIcon

MyQuestionIcon

185

You visited us 185 times! Enjoying our articles? Unlock Full Access!

The Problem of Areas

If dydx=xy+...

Question

If $\frac{d y}{d x} = x y + 2 x + 3 y + 6$ , then find the value of $y (- 1) - e^{2} y (- 3)$ .

A

e^{2} - 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

e^{2} + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

2 (e^{2} - 1)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

- 2 (e^{2} - 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2 (e^{2} - 1)$
$\frac{d y}{d x} = (x + 3) (y + 2)$ , If $X = x + 3, Y = y + 2$
$\frac{d Y}{Y} = X d X$
$\Rightarrow Y = A . e^{X^{2} / 2}, y = - 2 + A e^{(x + 3)^{2} / 2}$
$y (- 1) = - 2 + A e^{2}, y (- 3) = - 2 + A$
$y (- 1) - e^{2} y (- 3) = - 2 + 2 e^{2} = 2 (e^{2} - 1)$

Suggest Corrections

thumbs-up

0

Similar questions

\frac{4}{1 +} \frac{6}{2 +} \frac{8}{3 +} \dots \frac{2 n + 2}{n +} \dots = \frac{2 (e^{2} - 1)}{e^{2} + 1}

f (x)

is a function satisfying

f^{'} (x) = f (x)

f (0) = 1

g (x)

be another function such that

f (x) + g (x) = x^{2}

, then the value of

1 \int 0 f (x) g (x) d x

y = y (x)

be the solution of the differential equation

\frac{d y}{d x} + 2 y = f (x),

f (x) = {\begin{matrix} 1, x \in [0, 1] 0, otherwise \end{matrix}

y (0) = 0

y (\frac{3}{2})

Q. If the curves y = 2 e^x and y = ae^−x intersect orthogonally, then a =

(a) 1/2
(b) −1/2
(c) 2
(d) 2e²

No/2 atoms of $X_{(g)}$ are converted into $X_{(g)^{+}}^{+}$ by energy $E_{1}$ , No/2 atoms of $X_{g}$ are converted into $X_{(g)}^{-}$ by energy $E_{2}$ . Hence ionization potential and electron affinity of $X_{(g)}$ per atom are

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integration

PHYSICS

Watch in App

explore_more_icon

Explore more

The Problem of Areas

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon