Engineering Mat...

The equation \(\frac{{{{\rm{d}}^3}{\rm{y}}}}{{{\rm{d}}{{\rm{x}}^3}}} + {\left( {\frac{{{{\rm{d}}^2}{\rm{y}}}}{{{\rm{d}}{{\rm{x}}^2}}}} \right)^2} + \frac{{4{\rm{dy}}}}{{{\rm{dx}}}} + 5{{\rm{y}}^4} = 0\) has the degree

Let \(\frac{y}{{A\left( x \right)}} = \log x + C\) Where C is an arbitrary constant, is a solution of

\(\left( {{x^3} - x} \right)\frac{{dy}}{{dx}} - \left( {3{x^2} - 1} \right)y = {x^5} - 2{x^3} + x\)

Equation (α xy³ + y cos x) dx + (x²y² + β sin x) dy = 0 is exact if

The general solution of the differential equation \(\frac{{{d^4}y}}{{d{x^4}}} - 2\frac{{{d^3}y}}{{d{x^3}}} + 2\frac{{{d^2}y}}{{d{x^2}}} - 2\frac{{dy}}{{dx}} + y = 0\) is

General solution of (D² + a²)y = sin a x is y = C₁ cos ax + C₂ sin ax + A(x)

The solution of differential equation

Solve \(\frac{{{d^2}y}}{{d{y^2}}} - 3\frac{{dy}}{{dx}} + 2y = x{e^{3x}}\)

If x^r is on integrating factor of (x + y³) dx + 6xy² dy = 0, then r is ______

The differential equation \(y'' - 6y' + 9y = \frac{{{e^{3x}}}}{{{x^2}}}\) is solving by the method of variation of parameters, then Wronskian will be –

Wronskian for solution y = c₁y₁(t) + c₂y₂(t) is defined as \(W(y_1,y_2)(x) = \left| {\begin{array}{*{20}{c}} {{y_1}}&{{y_2}}\\ {y_1'}&{y_2'} \end{array}} \right| \)

The differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constants is: