Class 12

Math

Calculus

Differential Equations

If\displaystyle{y}={e}^{\text{tan}}^{\left({\left(-{1}\right)}\text{x}\right)},prove that $(1+x_{2})y_{2}+(2x−1)y_{1}=0.$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) $y=ae_{x}+be_{−x}+x_{2}$ : $xdx_{2}d_{2}y +2ydxdy −xy+x_{2}−2=0$

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 $x_{2}−y_{2}=cx$.

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y=ae_{3x}+be_{−2x}$

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

Find the equation of a curve passing through the point (0, 0) and whose differentialequation is $y_{prime}=exsinx$

Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Show that the general solution of the differential equation $dxdy +x_{2}+x+1y_{2}+y+1 =0$ is given by $(x+y+1)=A(1−x−y−2xy)$ where A is a parameter

Find the general solution of the differential equations:$dydx +xy =x_{2}$