Class 12

Math

Calculus

Differential Equations

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: $y=xsinx$ : $xyprime=y+xx_{2}−y_{2} (x=0$and$x>yorx<y$)

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The differential equation of all non-horizontal lines in a plane is

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A curve $y=f(x)$ passes through $(1,1)$ and tangent at $P(x,y)$ cuts the x-axis and y-axis at $A$ and $B$ , respectively, such that $BP:AP=3,$ then (a) equation of curve is $xy_{prime}−3y=0$ (b) normal at $(1,1)$ is $x+3y=4$ (c) curve passes through $2,8$ (d) equation of curve is $xy_{prime}+3y=0$

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Find the order and degree (if defined) of the equation: $a=dx_{2}d_{2}y 1[1+(dxdy )_{2}]_{23} ,$ where $a$ is constant

If $y=a_{2}−b_{2} 1 cos_{−1}(a+bcosxacosx+b ),$ then $dx_{2}d_{2}y =$ (i) $(a+bcosx)_{2}bsinx $ (ii) $−(a+bcosx)_{2}bsinx $ (iii) $(a+bcosx)_{2}bcosx $ (iii) $−(a+bcosx)_{2}bcosx $

The solution of the differential equation $dxdy =x_{2}−2x_{3}y_{3}3x_{2}y_{4}+2xy $ is