Class 12

Math

Calculus

Differential Equations

The differential equations, find a particular solution satisfying the given condition: $(x_{3}+x_{2}+x+1)dxdy =2x_{2}+x;y=1$when $x=0$

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Number of values of $m∈N$ for which $y=e_{mx}$ is a solution of the differential equation $dx_{3}d_{3}y −3dx_{2}d_{2}y −4dxdy +12y=0$ (a) 0 (b) 1 (c) 2 (d) More than 2

The solution of the differential equation $y_{prime}y_{primeprimeprime}=3(y_{primeprime})_{2}$ is

Statement 1 : The differential equation of all circles in a plane must be of order 3. Statement 2 : There is only one circle passing through three non-collinear points.

Solve: $1+x_{2}+y_{2}+x_{2}y_{2} +xydxdy =0$

A function $y=f(x)$ satisfies $(x+1)f_{prime}(x)−2(x_{2}+x)f(x)=(x+1)(e_{x})_{2} ,∀x≻1.$ If $f(0)=5,$ then $f(x)$ is

An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity with constant of proportionality as $k>0$ , and acts in a direction opposite to motion $(g=9.8s_{2}m )˙$ Then velocity cannot exceed.

The curve passing through the point $(1,1)$ satisfies the differential equation $dxdy +xy(x_{2}−1)(y_{2}−1) =0$ . If the curve passes through the point $(2 ,k),$ then the value of $[k]$ is (where [.] represents greatest integer function)_____

Statement 1 : Order of a differential equation represents the number of arbitrary constants in the general solution. Statement 2 : Degree of a differential equation represents the number of family of curves.