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Separable equation that integrates to inverse tan of y

This type of question, asked 4 times: 29 Jun 2022, 29 Jan 2024, 8 Apr 2024, 4 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    29 Jun 2022

    159
    If y=y(x)y = y(x) is the solution of the differential equation (1+e2x)dydx+2(1+y2)ex=0\left( 1 +e^{2x} \right)\frac{dy}{dx}+ 2\left( 1 +y^{2} \right)e^{x}= 0 and y(0)=0y(0) = 0, then 6(y′(0)+(y(log⁡e3))2)6\left( y^{'}(0) +\left( y\left( \log_{e}\sqrt{3} \right) \right)^{2} \right) is equal to:

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  2. Question 2

    29 Jan 2024

    86
    If the solution curve y=y(x)y = y(x) of the differential equation (1+y2)(1+log⁡ex)dx+xdy=0,x>0\left( 1 +y^{2} \right)\left( 1 +\log_{e}x \right)dx + xdy = 0,x > 0 passes through the point (1,1)(1,1) and y(e)=α−tan⁡(32)β+tan⁡(32)y(e) =\frac{\alpha - \tan\left( \frac{3}{2} \right)}{\beta + \tan\left( \frac{3}{2} \right)}, then α+2β\alpha + 2\beta is

  3. Question 3

    8 Apr 2024

    79
    Let y=y(x)y=y(x) be the solution of the differential equation (1+y2)etan⁡xdx+cos⁡2x(1+e2tan⁡x)dy=0\left( 1 +y^{2} \right)e^{\tan x}dx+\cos^{2}x\left( 1 +e^{2\tan x} \right)dy= 0, y(0)=1y(0) = 1. Then y(π4)y\left( \frac{\pi}{4} \right) is equal to:

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  4. Question 4

    4 Apr 2026 S1

    70
    Let y=y(x)y=y(x) be the solution of the differential equation dydx=(1+x+x2)(1−y+y2),y(0)=12\frac{dy}{dx}=\left( 1 + x +x^{2} \right)\left( 1 - y +y^{2} \right),y(0) =\frac{1}{2}. Then ( 2y(1)−12y(1) - 1 ) is equal to

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