1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Let a curve y = y(x) be given by the solution of the differential equation $$\cos \left( {{1 \over 2}{{\cos }^{ - 1}}({e^{ - x}})} \right)dx = \sqrt {{e^{2x}} - 1} dy$$. If it intersects y-axis at y = $$-$$1, and the intersection point of the curve with x-axis is ($$\alpha$$, 0), then e$$\alpha$$ is equal to __________________.
2
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let y = y(x) be the solution of the differential equation

xdy $$-$$ ydx = $$\sqrt {({x^2} - {y^2})} dx$$, x $$\ge$$ 1, with y(1) = 0. If the area bounded by the line x = 1, x = e$$\pi$$, y = 0 and y = y(x) is $$\alpha$$e2$$\pi$$ + $$\beta$$, then the value of 10($$\alpha$$ + $$\beta$$) is equal to __________.
3
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Let the curve y = y(x) be the solution of the differential equation, $${{dy} \over {dx}}$$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $${{4\sqrt 8 } \over 3}$$, then the value of y(1) is equal to _________.
4
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The difference between degree and order of a differential equation that represents the family of curves given by $${y^2} = a\left( {x + {{\sqrt a } \over 2}} \right)$$, a > 0 is _________.