Class 12

Math

Calculus

Differential Equations

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=cosx+C$ : $yprime+sinx=0$

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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

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.

Integrating factor of differential equation $cosxdxdy +ysinx=1$ is

Let the function $lnf(x)$ is defined where $f(x)$ exists for $x≥2andk$ is fixed positive real numbers prove that if $dxd (x.f(x))≥−kf(x)$ then $f(x)≥Ax_{−1−k}$ where A is independent of x.

From the differential equation of family of lines situated at a constant distance p from the origin.

If $∫_{a}ty(t)dt=x_{2}+y(x),$ then find $y(x)$

The curve satisfying the equation $dxdy =x(y_{3}−x)y(x+y_{3}) $ and passing through the point $(4,−2)$ is

Show that the differential equation $(x_{2}+xy)dy=(x_{2}+y_{2})dx$ is homogenous and solve it.