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 ______.

Which of the following is the homogeneous differential equation?

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

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

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

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

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

The differential equation of x² + y² = a² ______.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 ______.

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

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