A function y=f(x) satisfies the differential equation dydx−y=cosx−sinx with initial condition that y is bounded when x→∞. The area enclosed by y=f(x),y=cosx and the y-axis is

2√−1

2√

12√

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A function y=f(x) satisfies the differential equation dydx−y=cosx−sinx with initial condition that y is bounded when x→∞. The area enclosed by y=f(x),y=cosx and the y-axis is

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[a] IF =e−x ∴ye−x=∫e−x(cosx−sinx)dx Put −x=t =−∫et(cost+sint)dt=−etsint+c ye−x=e−xsinx+c Since, y is bounded when x→∞⇒c=0 ∴y=sinx Area =∫π/40(cosx−sinx)dx=2√−1

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Question Text	A function y=f(x) satisfies the differential equation dydx−y=cosx−sinx with initial condition that y is bounded when x→∞. The area enclosed by y=f(x),y=cosx and the y-axis is
Answer Type	Text solution:1
Upvotes	150

A function y=f(x) satisfies the differential equation dydx−y=cosx−sinx with initial condition that y is bounded when x→∞. The area enclosed by y=f(x),y=cosx and the y-axis is

Text solutionVerified

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