Differential Equations

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

Ques. 1JEE 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

Answer

(1) 31+(8)1/4

Solution

dyy(y-3)= dxx2-4

13 | y-3y |= 14 | x-2x+2 |+C

x=4, y= 32: 0= 14 13+C C= 14 3

x=10: 13 | y-3y |= 14 (3 812 )= 14 2

| y-3y |=23/4=(8)1/4

∵ slope never zero, y never reaches 0 or 3; y(4)= 32 0<y<3

3-yy=(8)1/4

y(10)= 31+(8)1/4

Answer: (1)

Keep practising — Differential Equations

Ques. 2JEE 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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