class 12

Math

Calculus

Differential Equations

Let $f:(0,∞)→R$ be a differentiable function such that $f_{′}(x)=2−xf(x) $ for all $x∈(0,∞)$ and $f(1)=1$, then

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Consider the equation $a_{2}+λx_{2} +b_{2}+λy_{2} =1,$ where a and b are specified constants and $λ$ is an arbitrary parameter. Find a differential equation satisfied by it.

The differential equation representing the family of curves $y_{2}=2c(x+c ),$ where $c$ is a positive parameter, is of (A) order 1 (B) order 2 (C) degree 3 (D) degree 4

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

The equation of the curve satisfying xdy−ydx=x2−y2−−−−−−√ and y(1)=0 is:

The general solution of the differential equation dydx−tany1+x=(1+x)exsecy is

The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2 is

Find the curve for which the length of normal is equal to the radius vector.

What is the solution of satisfying?