Class 12

Math

Calculus

Differential Equations

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

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The solution of the differential equation $x_{2}dxdy cos(x1 )−ysin(x1 )=−1,$ where $y→−1$ as$x→∞$ is

The gradient of the curve passing through (4, 0) is given by if the point (5, a) lies on the curve, then the value of a is

The order of the differential equation whose general solution is given by $y=(C_{1}+C_{2})cos(x+C_{3})−C_{4}e_{x+C_{5}},$ where $C_{1},C_{2},C_{3},C_{4},C_{5}$ , are arbitrary constants, is (a) 5 (b) 4 (c) 3 (d) 2

The degree of differential equation satisfying the relation1+x2−−−−−√+1+y2−−−−−√=λ(x1+y2−−−−−√−y1+x2−−−−−√) is

The differential equation of the curve xc−1+yc+1=1 is given by

The solution to of the differential equation(x+1)dydx−y=e3x(x+1)2 is

The solution of is

Solve $dxdy 1+x+y =x+y−1$