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Separable equation with a condition: value of y at a point

This type of question, asked 5 times: 2 May 2023 S2, 11 May 2023 S2, 12 May 2024 S2, 19 Apr 2025 S1, 22 Apr 2025 S1. All 6 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    127
    If (2+sin⁡x)dydx+(y+1)cos⁡x=0(2+\sin x)\frac{dy}{dx} + (y+1)\cos x = 0 and y(0)=1y(0)=1, then y ⁣(π2)y\!\left(\frac{\pi}{2}\right) is equal to

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  2. Question 2

    2 May 2023 S2

    121
    If (5+ex)2+ydydx+ex=0(5+e^x)^{2+y}\frac{dy}{dx} + e^x = 0 satisfying y(0)=1y(0)=1, then a value of y(log⁡13)y(\log 13) is

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  3. Question 3

    11 May 2023 S2

    138
    If y(x)y(x) is the solution of the differential equation (x+2)dydx=x2+4x−9, x≠−2(x+2)\frac{dy}{dx} = x^2+4x-9,\ x\neq-2 and y(0)=0y(0)=0, then y(−4)y(-4) is equal to

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  4. Question 4

    12 May 2024 S2

    130
    If (2+sin⁡x)dydx+(y+1)cos⁡x=0(2+\sin x)\frac{dy}{dx} + (y+1)\cos x = 0 and y(0)=1y(0) = 1, then y ⁣(π2)y\!\left(\frac{\pi}{2}\right) is

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  5. Question 5

    19 Apr 2025 S1

    117
    If y=y(x)y=y(x) satisfies (2+sin⁡x1+y)dy dx=−cos⁡x\left( \frac{2 + \sin x}{1 +y} \right)\frac{dy}{\text{ }dx}= - \cos x. such that y(0)=2y(0) = 2, then y(π2)y\left( \frac{\pi}{2} \right) is equal to

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  6. Question 6

    22 Apr 2025 S1

    101
    If y=y(x)y=y(x) and (2+sin⁡xy+1)dy dx=−cos⁡x,y(0)=1\left( \frac{2 + \sin x}{y+ 1} \right)\frac{dy}{\text{ }dx}= - \cos x,y(0) = 1, then y(π2)=y\left( \frac{\pi}{2} \right)=

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