Class 12

Math

Calculus

Differential Equations

If $xdxdy =y(gy−gx+1)$, then the solutions of the equation is

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The general solution of the differential equation $yydx−xdy =0$is(A) $xy=C$ (B) $x=Cy_{2}$ (C) $y=Cx$ (D) $y=Cx_{2}$

If $y=3cos(gx)+4sin(gx),$then show that $x_{2}dx_{2}d_{2}y˙ +dxdy +y=0$

Write the sum of the order and degree of the differential equation $1+(dxdy )_{4}=7(dx_{2}d_{2} )_{3}$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=cosx+C$ : $yprime+sinx=0$

Solve the following differential equation: $(1+x_{2})dy+2xydx=cotxdx;x=0$

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20, 000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=e_{x}+1:yprimeprime−yprime=0$