A complete solution of partial differential equation \(\frac {\partial z}{\partial x} - 3x^2 = \left(\frac {\partial z}{\partial y}\right)^2 - y\) will be ________, where a and b are arbitrary constants.

z1 / 2 = (x + a)1 / 2 + (y + b)1 / 2

\(z = ax + x^3 + \left(\frac 2 3\right) (a + y)^{\frac 3 2} + b\)

A complete solution of partial differential equation \(\frac {\partia

1.	A complete solution of partial differential equation \(\frac {\partial z}{\partial x} - 3x^2 = \left(\frac {\partial z}{\partial y}\right)^2 - y\) will be ________, where a and b are arbitrary constants.
A.	z2 = ax2 + by2 + 1
B.	\(z = ax + x^3 + \left(\frac 2 3\right) (a + y)^{\frac 3 2} + b\)
C.	z1 / 2 = (x + a)1 / 2 + (y + b)1 / 2
D.	z = (ax2 + by2)3 / 2 + 2
Answer» C. z1 / 2 = (x + a)1 / 2 + (y + b)1 / 2

For \(\frac{{{d^2}y}}{{d{x^2}}} + 4\frac{{dy}}{{dx}} + 3y = 3{e^{2x}}\), the particular integral is :
Consider the differential equation given below:\(\dfrac{dy}{dx} + \dfrac{x}{1-x^2} y= x\sqrt{y}\)The integrating factor of the differential equation is:
General solution of the equation (x3 + 3xy2)dx + (3x2y + y3)dy = 0 is (c is a constant)
For the equation \(\frac{{dy}}{{dx}} + 7{x^2}y = 0\), if y(0) = \(\frac{{3}}{{7}}\), then the value of y(1) is
If \(\rm \dfrac{d^2y}{dx^2}+\sin x = 0\), then the solution of this differential equation is -
\(\frac{{{\partial ^2}u}}{{\partial {t^2}}} = {c ^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}}\) represents the equation for
Consider the following partial differential equation for with the constant c > 1:Solution of this equation is \(\frac{{\partial u}}{{\partial y}} + c\frac{{\partial u}}{{\partial x}} = 0\)
Determine the degree and order of the given differential equation respectively. \({\rm{y}} = {\rm{x}}{\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} + {\left( {\frac{{{\rm{dx}}}}{{{\rm{dy}}}}} \right)^2}?\)
If the characteristic equation of the differential equation \(\frac{{{d^2}y}}{{d{x^2}}} + 2\alpha \frac{{dy}}{{dx}} + y = 0\) has two equal roots, then the values of α are
A particle starts from origin with a velocity (in m/s) given by the equation \(\rm \frac{dx}{dt}=x+1\). The time (in seconds) taken by the particle to traverse a distance of 24 m is: