Let f: R R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation dy dx =(2+5y)(5y-2), then the value of _ x - f(x) is _____.

JEE Advanced 2018 Mathematics question

Let be a differentiable function with . If satisfies the differential equation

=(2+5y)(5y-2),

then the value of is .

Answer: 0.4

has constant solutions . Starting from , which lies between them, , and stays in ,

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Question ID VK-026799