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Engineering

Let a curve $y = f(x)$ pass through the points $(0, 5)$ and $(\log_e 2, k)$ . If the curve satisfies the differential equation $2(3 + y)e^{2x}dx – (7 + e^{2x})dy = 0$ , then $k$ is equal to

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A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is: [Diagram: Semicircular arc with mass m at center]

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Questions

Let a curve y=f(x)y = f(x)y=f(x) pass through the points (0,5)(0, 5)(0,5) and (log⁡e2,k)(\log_e 2, k)(loge​2,k). If the curve satisfies the differential equation 2(3+y)e2xdx–(7+e2x)dy=02(3 + y)e^{2x}dx – (7 + e^{2x})dy = 02(3+y)e2xdx–(7+e2x)dy=0, then kkk is equal to

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Questions

Let a curve y=f(x)y = f(x)y=f(x) pass through the points (0,5)(0, 5)(0,5) and (log⁡e2,k)(\log_e 2, k)(loge​2,k). If the curve satisfies the differential equation 2(3+y)e2xdx–(7+e2x)dy=02(3 + y)e^{2x}dx – (7 + e^{2x})dy = 02(3+y)e2xdx–(7+e2x)dy=0, then kkk is equal to

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Let a curve $y = f(x)$ pass through the points $(0, 5)$ and $(\log_e 2, k)$ . If the curve satisfies the differential equation $2(3 + y)e^{2x}dx – (7 + e^{2x})dy = 0$ , then $k$ is equal to

Let a curve $y = f(x)$ pass through the points $(0, 5)$ and $(\log_e 2, k)$ . If the curve satisfies the differential equation $2(3 + y)e^{2x}dx – (7 + e^{2x})dy = 0$ , then $k$ is equal to