First Order ODEs Mock Tests

5 questions available

First Order ODEs Mock Test 1

Questions: 5

GATE Mathematics

The solution of the differential equation xdy/dx = y + x·sin(y/x) is

A y = x·sin⁻¹(Cx)

B y = x·sin(Cx)

C y = x·cos⁻¹(Cx)

D y = Cx

GATE Mathematics

The order and the degree of the differential equation d²y/dx² + (dy/dx)³ + sin(dy/dx)¹ᐟ³ + 1 = 0 are respectively

A 2 and 3

B 2 and 6

C 2 and not defined

D 3 and 2

GATE Mathematics

The solution of the differential equation dy/dx = y/x with y(1) = 2 is

A y = 2x

B y = x²

C y = 2/x

D y = ln(x) + 2

GATE Mathematics

The solution of the differential equation dy/dx = y + eˣ with y(0) = 0 is

A y = (x − 1)eˣ + eˣ

B y = (x − 1)eˣ

C y = xeˣ

D y = eˣ − 1

GATE Mathematics

The solution of the differential equation dy/dx = (x + y)² using the substitution u = x + y is

A tan(x + y) = x + C

B tan(u) = x + C where u = x + y

C tan(x + y) = x + C

D −tan(x + y) = x + C