Differential Equations

JEE Main 2025 (Online) 23rd January Evening ShiftMCQHard📈 Topic in 11% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

Let x=x(y) be the solution of the differential equation y= (x-y dxdy ) ( xy ), y>0 and x(1)= 2. Then (x(2)) is equal to :

2 ( e 2 )-1
1-2 ( e 2 )2
1-2 ( e 2 )
2 ( e 2 )2-1

Answer

(4) 2 ( e 2 )2-1

Solution

y dy=(x dy-y dx) xy

dyy=- xy d(x/y) (as x dy-y dx=-y2 d(x/y))

Integrate: y= xy+C; x(1)= 2 C=0

At y=2: x(2)2= 2

x(2)=2 2 x(2)2-1=2( 2)2-1

Answer: (4)

Keep practising — Differential Equations

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let x=x(y) be the solution of the differential equation y2 dx+ (x- 1y )dy=0. If x(1)=1, then x ( 12 ) is :

32+e
12+e
3+e
3-e

Ques. 3JEE Main 2025, 22 January (Evening Shift)

If x=f(y) is the solution of the differential equation (1+y2 )+ (x-2e -1y ) dydx=0, y (- 2, 2 ) with f(0)=1, then f ( 1 3 ) is equal to :

e /4
e /12
e /6
e /3

Ques. 4JEE Main 2025, 22 January (Evening Shift)

Let y=f(x) be the solution of the differential equation dydx+ xyx2-1= x6+4x 1-x2, -1<x<1 such that f(0)=0. If 6 -1/21/2f(x) dx=2 - then 2 is equal to .

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