Differential Equations

JEE Main 2024 (Online) 27th January Morning ShiftMCQMedium📈 Topic in 33% papers+4−1

Ques. 1JEE Main 2024, 27 January (Morning Shift)

Let x=x(t) and y=y(t) be solutions of the differential equations dxdt+ax=0 and dydt+by=0 respectively, a, b . Given that x(0)=2; y(0)=1 and 3y(1)=2x(1), the value of t, for which x(t)=y(t), is :

Answer

(2) 432

Solution

Separate variables: dxx=-a dt

x=x(0)e-at=2e-at

Similarly y=y(0)e-bt=e-bt

3y(1)=2x(1) 3e-b=4e-a ea-b= 43

x(t)=y(t) 2e-at=e-bt e(a-b)t=2

( 43 )t=2 t= 432

Answer: (2)

Keep practising — Differential Equations

Ques. 2JEE Main 2024, 27 January (Morning Shift)

If the solution of the differential equation (2x+3y-2) dx+(4x+6y-7) dy=0, y(0)=3, is x+ y+3 e|2x+3y- |=6, then +2 +3 is equal to .

Ques. 3JEE Main 2024, 27 January (Evening Shift)

If y=y(x) is the solution curve of the differential equation (x2-4 )dy- (y2-3y )dx=0, x>2, y(4)= 32 and the slope of the curve is never zero, then the value of y(10) equals :

31+(8)1/4
31-(8)1/4
31-2 2
31+2 2

Ques. 4JEE Main 2024, 27 January (Evening Shift)

If the solution curve, of the differential equation dydx= x+y-2x-y passing through the point (2,1) is -1 ( y-1x-1 )- 1 e ( + ( y-1x-1 )2 )= e|x-1|, then 5 + is equal to .

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