Mathematics Tes...

The order and degree of the differential equation \({\left( {\frac{{{d^4}y}}{{d{x^4}}}} \right)^{\frac{1}{2}}} = {\left[ {1 + {{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)}^2}} \right]^{\frac{1}{3}}}\) respectively are

The differential equation of all lines passing through the origin is:

The general solution y(x) of the differential equation 

\(\rm {dy\over dx}= {\sqrt{1-y^2}\over \sqrt{1-x^2}}\)

Find the integrating factor of the following differential equation.

Solve (2y + x) \(\rm dy\over dx\) = 1

Find the general solution of the differential equation \(ydx = \left( {y - x} \right)dy\)

For the equation \(\frac{{dy}}{{dx}} + 7{x^2}y = 0\), if y(0) = \(\frac{{3}}{{7}}\), then the value of y(1) is

Solve the initial value problem, dy = e^{x + 2y} dx , y (0) = 0. 

If \(x\frac{dy}{dx}=y(\log y-\log x+1)\), then the solution of the equation is

What is the general solution of the differential equation x² dy + y² dx = 0 ?

Where c is the constant of integration