1
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 _________.
2
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 _________.
3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
If y = y(x) is the solution of the equation

$${e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x$$, y(0) = 0; then

$$1 + y\left( {{\pi \over 6}} \right) + {{\sqrt 3 } \over 2}y\left( {{\pi \over 3}} \right) + {1 \over {\sqrt 2 }}y\left( {{\pi \over 4}} \right)$$ is equal to ____________.
4
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
If the curve, y = y(x) represented by the solution of the differential equation (2xy2 $$-$$ y)dx + xdy = 0, passes through the intersection of the lines, 2x $$-$$ 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to _________.