Solution of differential equation d y-d x-tan y-x-x ex y isA- x2sin y-exx-12-ex-CB- x sin y-exx-12-CC- x sin y-exx2-2 x-2-CD- x sin y-exx-12-ex-C

The correct option is C x sin y = e^x (x^2 2x + 2) + C dy/dx+sin y/x cos y=xe^x/cos y ⇒ xcos y dy/dx+sin y=x^2e^x ⇒ xcos y dy+sin y dx=x^2e^xdx ⇒∫ d(xsin y)= ...

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Byju's Answer

Standard XII

Mathematics

General Solution of a Differential Equation

Solution of d...

Question

Solution of differential equation $\frac{d y}{d x} + \frac{tan y}{x} = x e^{x} sec y$ is

$x sin y = e^{x} (x^{2} - 2 x + 2) + C$

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$x sin y = e^{x} (x + 1)^{2} + e^{x} + C$

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$x^{2} sin y = e^{x} (x - 1)^{2} + e^{x} + C$

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$x sin y = e^{x} (x + 1)^{2} + C$

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Solution

The correct option is A
$x sin y = e^{x} (x^{2} - 2 x + 2) + C$

$\frac{d y}{d x} + \frac{sin y}{x cos y} = \frac{x e^{x}}{cos y}$

$\Rightarrow x cos y \frac{d y}{d x} + sin y = x^{2} e^{x}$

$\Rightarrow x cos y d y + sin y d x = x^{2} e^{x} d x$

$\Rightarrow \int d (x sin y) = \int x^{2} e^{x} d x$

$\Rightarrow x sin y = e^{x} (x^{2} - 2 x + 2) + C$

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Similar questions

equals

A. − cot (ex^x) + C

B. tan (xe^x) + C

C. tan (e^x) + C

D. cot (e^x) + C

Q. The value of

\int \frac{e^{x} (1 + x) d x}{{cos}^{2} (e^{x} x)}

$\int \frac{x + 3}{{(x + 4)}^{2}} e^{x} d x =$

(a) $\frac{e^{x}}{x + 4} + C$

(b) $\frac{e^{x}}{x + 3} + C$

(c) $\frac{1}{{(x + 4)}^{2}} + C$

(d) $\frac{e^{x}}{{(x + 4)}^{2}} + C$

$\int \frac{e^{x} (x - 1) (x - l n x)}{x^{2}} d x$ is equal to

\frac{d y}{d x} + x sin y = ln x

is a linear differential equation of first order.

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Solution of differential equation dydx+tanyx=xexsecy is

The correct option is A xsiny=ex(x2−2x+2)+C dydx+sinyxcosy=xexcosy ⇒xcosydydx+siny=x2ex ⇒xcosydy+sinydx=x2exdx ⇒∫d(xsiny)=∫x2exdx ⇒xsiny=ex(x2−2x+2)+C

Solution of differential equation $\frac{d y}{d x} + \frac{tan y}{x} = x e^{x} sec y$ is