JEE Main Mathematics: Differential Equations Practice Questions

15 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$F in d t h e g e n er a l so l u t i o n o f t h e d i f f er e n t ia l e q u a t i o n d y / d x = e^{(} x + y) .$
Easy
Q2.
$The solution of the differential equation dy/dx = 1 is:$
Easy
Q3.
$W ha t i s t h e in t e g r a t in g f a c t or o f t h e d i f f er e n t ia l e q u a t i o n d y / d x + y = e^{x} ?$
Easy
Q4.
$W ha t i s t h eor d er an dd e g r eeo f t h e d i f f er e n t ia l e q u a t i o n d 2 y / d x 2 + (d y / d x)^{3} + y = 0 ?$
Easy
Q5.
$Which of the following is a linear differential equation?$
Easy
Q6.
$T h eso l u t i o n o f t h e d i f f er e n t ia l e q u a t i o n d y / d x = e^{(} x - y) + x^{2} e^{(} - y) i s :$
Medium
Q7.
$F in d t h eor d er an dd e g r eeo f t h e d i f f er e n t ia l e q u a t i o n d^{2} y / d x^{2} = (1 + (d y / d x)^{2})^{(} 3/2) .$
Medium
Q8.
$T h e g e n er a l so l u t i o n o f t h e d i f f er e n t ia l e q u a t i o n d y / d x + y / x = x^{2} i s :$
Medium
Q9.
$Find the solution of the differential equation dy/dx = (x + y) / (x - y) with the initial condition y(1) = 0.$
Medium
Q10.
$What is the integrating factor of the differential equation dy/dx + y tan x = sec x?$
Medium
Q11.
$F in d t h eso l u t i o n o f t h e d i f f er e n t ia l e q u a t i o n (x^{2} + y^{2}) d x - 2 x y d y = 0 g i v e n t ha t y (1) = 1.$
Hard
Q12.
$S o l v e t h e d i f f er e n t ia l e q u a t i o n (d y / d x)^{2} - (e^{x} + e^{-} x) d y / d x + 1 = 0.$
Hard
Q13.
$T h ec u r v e p a ss in g t h r o ug h (1, 2) s a t i s f y in g t h e d i f f er e n t ia l e q u a t i o n x d y / d x = y + x^{2} s in (x) i s g i v e nb y y = f (x) . F in df (p i) .$
Hard
Q14.
$F in d t h eor t h o g o na l t r aj ec t or i eso f t h e f ami l y o f c u r v es y^{2} = 4 a x .$
Hard
Q15.
$If y(x) satisfies the differential equation dy/dx + y tan(x) = sec(x) and y(0) = 0, then find the value of y(pi/4).$
Hard

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