Differential Equations

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

Ques. 1JEE 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 .

Answer

Solution

Put 2x+3y=t ⇒ 2+3 dydx= dtdx, and dydx=- t-22t-7

⇒ dtdx=2- 3(t-2)2t-7= t-82t-7

⇒ (2+ 9t-8 )dt= dx ∵ 2t-7t-8=2+ 9t-8

⇒ 2t+9 |t-8|=x+C

x=0, y=3: t=9 ⇒ C=18

⇒ 4x+6y+9 |2x+3y-8|=x+18

⇒ x+2y+3 |2x+3y-8|=6 (÷3)

∴ =1, =2, =8 ⇒ +2 +3 =1+4+24=29

Answer: 29

Keep practising — Differential Equations

Ques. 2JEE 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. 3JEE 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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