The solution of 1-x2dy-dx-2xy - cos x is-

The correct option is D (1+x^2)y = sin x + c (1+x^2)dydx+2xy=cosx ⇒ #160;ddx(y(1+x^2))=cos x ⇒∫ d(y(1+x^2)) =∫cos xdx+c ⇒ #160;y(1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Basic Inverse Trigonometric Functions

The solution ...

Question

The solution of $(1 + x^{2}) \frac{d y}{d x} + 2 x y = c o s x$ is:

y (1 + x^{2}) = c o s x + c

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

(1 + x^{2}) c o s x = y + c

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

(1 + x^{2}) y = s i n x + c

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

y (1 + x^{2}) + s e c x = c

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

Open in App

Solution

The correct option is D $(1 + x^{2}) y = s i n x + c$
$(1 + x^{2}) \frac{d y}{d x} + 2 x y = c o s x$

$\Rightarrow \frac{d}{d x} (y (1 + x^{2})) = cos x$

$\Rightarrow \int d (y (1 + x^{2})) = \int cos x d x + c$
$\Rightarrow y (1 + x^{2}) = sin x + c$

Suggest Corrections

Similar questions

The solution of differential equation $\frac{d y}{d x} + \frac{2 x y}{1 + x^{2}} = \frac{1}{(1 + x^{2})^{2}}$ is
(a) $y (1 + x^{2}) = C + t a n^{- 1} x$
(b) $\frac{y}{1 + x^{2}} = C + t a n^{- 1} x$
(c) $y l o g (1 + x^{2}) = C + t a n^{- 1} x$
(d) $y (1 + x^{2}) = C + s i n^{- 1} x$

Q. Match the elements of list I, which have differential equations, with elements of list II, which have solutions of differential equations:

List I	List II
A) $y y_{1} = {sec}^{2} x$	1) $y {sec}^{2} x = sec x + c$
B) $y_{1} = x sec y$	2) $x y = cos y + c$
C) $y_{1} + (2 y tan x) = sin x$	3) $x y = sin x + c$
D) $x y_{1} + y = cos x$	4) $y^{2} = 2 tan x + c$
	5) $x^{2} = 2 sin y + c$