Class 12

Math

Calculus

Differential Equations

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is $2xyx_{2}+y_{2} $, is given by $x_{2}−y_{2}=cx$.

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A normal at any point $(x,y)$ to the curve $y=f(x)$ cuts a triangle of unit area with the axis, the differential equation of the curve is

The solution of the equationx∫0xy(t)dt=(x+1)∫x0ty(t)dt,x>0 is

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

If $y(x)$ satisfies the differential equation $y_{prime}−ytanx=2xsecx$ and $y(0)=0$ , then

Solution of the differential equationdxdy−xlogx1+logx=ey1+logx′ if y(1)=0, is

Find the orthogonal trajectory of $y_{2}=4ax$ (a being the parameter).

if $a,b$ are two positive numbers such that $f(a+x)=b+[b_{3}+1−3b_{2}f(x)+3b{f(x)}_{2}−{f(x)}_{3}]_{31}$ for all real $x$, then prove that $f(x)$ is peroidic and find its peroid?

Solve $xdy=(y+xf_{prime}(xy )f(xy ) )dx$