The general solution of the differential equation d x d y + sin ( x + y ) = sin ( x − y ) is

The equation is, d x d y = sin ( x − y ) − sin ( x + y ) = 2 cos x sin ( − y ) ⇒ s i n y d y + 2 cos x d x = 0 ⇒ ∫ cos ecy d y + 2 ∫ cos x d x = C ⇒ lo g tan 2 y + 2 sin x = C

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableMedium2 minPYQ_2013

MathematicsMediumsingle choice

The general solution of the differential equation $\frac{d y}{d x} + sin (x + y) = sin (x - y)$ is

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Answer:

Solution:

The equation is, $\frac{d y}{d x} = sin (x - y) - sin (x + y) = 2 cos x sin (- y)$ $\Rightarrow \frac{d y}{s i n y} + 2 cos x d x = 0$ $\Rightarrow \int cos ecy d y + 2 \int cos x d x = C$ $\Rightarrow lo g tan \frac{y}{2} + 2 sin x = C$

Stream:BITSATSubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: PYQ_2013

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