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

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

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

The differential equation of x² + y² = a² ______.

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

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 ______.

Find the order and degree of the following differential equations.
\(\frac { dy }{ dx } +2y={ x }^{ 3 }\)

Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²

Solve: \(\frac { dy }{ dx } ={ ae }^{ y }\)

Find the curve whose gradient at any point P(x, y) on it is \(\frac { x-a }{ y-b } \) and which passes through the origin.

The slope of the tangent to a curve at any point (x, y) on it is given by (y³−2yx²)dx + (2xy²−x³)dy = 0 and the curve passes through (1, 2). Find the equation of the curve.

Solve the following:
\(\frac { dy }{ dx } +\frac { y }{ x } ={ xe }^{ x }\)

Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants

Solve the differential equation \(\frac { dy }{ dx } =\frac { x-y }{ x+y } \)

Solve \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +5y\) = 0

Solve: (3D² + D - 14)y = 4 - 13\({ e }^{\frac{-7}{3}x}\)

Solve sec²x tan y dx + sec²y tan x dy = 0

The sum of Rs. 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (log_e2 = 0.6931)

Solve (x² + 1)\(\frac { dy }{ dx } \) + 2xy = 4x²