Class 12

Math

Calculus

Differential Equations

Find the order and degree (if defined) of the equation: $dx_{4}d_{4}y +3(dx_{2}d_{2}y )_{6}+sinx=2cosx$

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The solution to the differential equation $ygy+xy_{prime}=0,$ where $y(1)=e,$ is

The solution to the differential equationdydx=yf′(x)−y2f(x) Where f(x) is a given function is

What is the degree of the differential equation(d3ydx3)2/3+4−3(d2ydx2)+5(dydx)=0?

Solve $dxdy =(x+y)_{2}$

A curve passing through (2, 3) and satisfying the differential equation ∫x0ty(t)dt=x2y(x),(x>0) is

Find the time required for a cylindrical tank of radius $r$ and height $H$ to empty through a round hole of area $a$ at the bottom. The flow through the hole is according to the law $v(t)=k2gh(t) $ , where $v(t)$ and $h(t)$ , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time $t,$ and $g$ is the acceleration due to gravity.

If xdy=ydx+y2dy,y>0 andy(1)=1, then what is y(−3) equal to?

Solve the equation $ydx+(x−y_{2})dy=0$