The solution of the differential equation dydx - 3e2x - 3e4xex - e-x is

The correct option is D y = e^3x + C Given differential equation is dydx = 3e^2x + 3e^4xe^x + e^ x = 3e^2x(1 + e^2x)· e^x(1 + e^2x) ⇒dydx = 3· e^ ...

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Standard XII

Mathematics

Integrating Factor

The solution ...

Question

The solution of the differential equation $\frac{d y}{d x} = \frac{3 e^{2 x} + 3 e^{4 x}}{e^{x} + e^{- x}}$ is

y = e^{3 x} + C

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y = 2 e^{2 x} + C

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y = e^{x} + C

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y = e^{4 x} + C

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y = 9 e^{3 x} + C

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Solution

The correct option is D $y = e^{3 x} + C$
Given differential equation is
$\frac{d y}{d x} = \frac{3 e^{2 x} + 3 e^{4 x}}{e^{x} + e^{- x}} = \frac{3 e^{2 x} (1 + e^{2 x}) \cdot e^{x}}{(1 + e^{2 x})}$
$\Rightarrow \frac{d y}{d x} = 3 \cdot e^{3 x}$
$\Rightarrow \int d y = \int 3 \cdot e^{3 x} d x$ (on integrating)
$\Rightarrow y = 3 \cdot \frac{e^{3 x}}{3} + C$
$\Rightarrow y = e^{3 x} + C$

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Similar questions

The general solution of the differential equation $\frac{d y}{d x} = e^{x + y}$ is
(a) $e^{x} + e^{- y} = C$
(b) $e^{x} + e^{y} = C$
(c) $e^{- x} + e^{y} = C$
(d) $e^{- x} + e^{- y} = C$

Q. The general solution of the differential equation

\frac{d y}{d x} = e^{x + y}

, is
(a) e^x+ e^−y = C
(b) e^x + e^y = C
(c) e⁻^x + e^y = C
(d) e^−x + e^−y = C

Q. Which of the following relation in x and y is general solution of the differential equation

\frac{d y}{d x} = y

Q. Which of the following relation in x and y is general solution of the differential equation

\frac{d y}{d x} = y

Q. Solve :

\frac{d y}{d x} = \frac{3 e^{2 x} + 3 e^{4 x}}{e^{x} + e^{- x}}

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The solution of the differential equation dydx=3e2x+3e4xex+e−x is

The correct option is D y=e3x+CGiven differential equation isdydx=3e2x+3e4xex+e−x=3e2x(1+e2x)⋅ex(1+e2x)⇒dydx=3⋅e3x⇒∫dy=∫3⋅e3xdx (on integrating)⇒y=3⋅e3x3+C⇒y=e3x+C

The solution of the differential equation $\frac{d y}{d x} = \frac{3 e^{2 x} + 3 e^{4 x}}{e^{x} + e^{- x}}$ is