The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.

(a)

1

(b)

2

(c)

3

(d)

4

The order and degree of the differential equation \(\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 } \) are respectively ______.

(a)

2 and 3

(b)

3 and 2

(c)

2 and 1

(d)

2 and 2

The order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}-\sqrt{\left(\frac{d y}{d x}\right)}-4=0\) are respectively ______.

(a)

2 and 6

(b)

3 and 6

(c)

1 and 4

(d)

2 and 4

The differential equation \({ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }\) = x is ______.

(a)

of order 2 and degree 1

(b)

of order 1 and degree 3

(c)

of order 1 and degree 6

(d)

of order 1 and degree 2

The differential equation formed by eliminating a and b from \(y=a e^{x}+b e^{-x}\) is ______.

(a)

\(\frac{d^{2} y}{d x^{2}}-y=0\)

(b)

\(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0\)

(c)

\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0\)

(d)

\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -x=0\)

The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\) is ______.

(a)

e^ഽPdx

(b)

^{\(\int P d x\)}

(c)

ഽPdy

(d)

e^ഽPdy

If y = cx + c− c³ then its differential equation is ______.

(a)

\(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

(b)

\(y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx } \)

(c)

\(\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx } \)

(d)

\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

The complementary function of (D²+ 4)y = e^2x is ______.

(a)

(Ax +B)e^2x

(b)

(Ax +B)e^−2x

(c)

A cos 2x + B sin 2x

(d)

Ae^−2x+ Be^2x

The differential equation of y = mx + c is ______.(m and c are arbitrary constants) 

(a)

\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \) = 0

(b)

y = x \(\frac { dy }{ dx } \) + c

(c)

xdy + ydx = 0

(d)

ydx − xdy = 0

The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.

(a)

\(\frac { { x }^{ 2 }{ e }^{ 4x } }{ 2! } \)

(b)

\(\frac { { e }^{ 4x } }{ 2! } \)

(c)

x²e^4x

(d)

xe^4x

Solution of \(\frac { dy }{ dx } \) + Px = 0 ______.

(a)

x = ce^py

(b)

x = ce^−py

(c)

x = py + c

(d)

x = cy

If sec² x is an integrating factor of the differential equation \(\frac { dy }{ dx } \) + Py Q then P = ______.

(a)

2 tan x

(b)

sec x

(c)

cos² x

(d)

tan² x

The integrating factor of x \(\frac { dy }{ dx } \) - y = x² is ______.

(a)

\(\frac {-1}{x}\)

(b)

\(\frac {1}{x}\)

(c)

log x

(d)

x

The solution of the differential equation \(\frac { dy }{ dx } \) + Py = Q where P and Q are the function of x is ______.

(a)

\(y=\int Q e^{\int P d x} d x+c\)

(b)

\(y=\int Q e^{-\int P d x} d x+c\)

(c)

\(y e^{\int P d x}=\int Q e^{\int P d x} d x+c\)

(d)

\(y e^{\int P d x}=\int Q e^{-\int P d x} d x+C\)

The differential equation formed by eliminating A and B from y = e^−2x(A cos x + B sin x) is ______.

(a)

y₂ − 4y₁ + 5 = 0

(b)

y₂+ 4y – 5 = 0

(c)

y₂−4y₁−5= 0

(d)

y₂ + 4y₁ + 5 = 0

The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)² ______.

(a)

\(\frac { { x }^{ 2 } }{ 2 } { e }^{ ax }\)

(b)

xe^ax

(c)

\(\frac { x }{ 2 } \)e^ax

(d)

x²e^ax

The differential equation of x² + y² = a² ______.

(a)

xdy + ydx = 0

(b)

ydx – xdy = 0

(c)

xdx – ydx = 0

(d)

xdx + ydy = 0

The complementary function of \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx } \) = 0 is ______.

(a)

A + Be^x

(b)

(A + B) e^x

(c)

(Ax + B) e^x

(d)

Ae^x + B

The P.I of (3D² + D − 14)y = 13e^2x is ______.

(a)

\(\frac {x}{2}\)e^2x

(b)

xe^2x

(c)

\(\frac {x^2}{2}\)e^2x

(d)

13xe^2x

The general solution of the differential equation \(\frac{dy}{dx}\) = cos x is ______.

(a)

y = sinx + 1

(b)

y = sinx - 2

(c)

y = cos x + c, c is an arbitrary constant

(d)

y = sin x + c, c is an arbitrary constant

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution, ______.

(a)

y = v x

(b)

v = y x

(c)

x = v y

(d)

x = v

A homogeneous differential equation of the form  \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.

(a)

x = v y

(b)

y = v x

(c)

y = v

(d)

x = v

The variable separable form of \(\frac { dy }{ dx } =\frac { y(x-y) }{ x(x+y) } \) by taking y = vx and \(\frac { dy }{ dx } =v+x\frac { dv }{ dx } \) is ______.

(a)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=\frac { dx }{ x } \)

(b)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=-\frac { dx }{ x } \)

(c)

\(\frac { 2{ v }^{ 2 } }{ 1-v } dv=\frac { dx }{ x } \)

(d)

\(\frac { 1+v }{ 2{ v }^{ 2 } } dv=-\frac { dx }{ x } \)

Which of the following is the homogeneous differential equation?

(a)

(3x−5)dx = (4y−1)dy

(b)

xy dx−(x³+y³)dy = 0

(c)

y²dx+(x² − xy  − y²)dy = 0

(d)

(x²+y)dx = (y²+x)dy

The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

(a)

\(f\left( \frac { y }{ x } \right) =k.x\)

(b)

\(xf\left( \frac { y }{ x } \right) =k\)

(c)

\(f\left( \frac { y }{ x } \right) =ky\)

(d)

\(yf\left( \frac { y }{ x } \right) =k\)