Class 12

Math

Calculus

Differential Equations

Solve $dxdy =x+2y−32x−y+1 $

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Find the order and degree (if defined) of the equation: $dx_{4}d_{4}y +3(dx_{2}d_{2}y )_{6}+sinx=2cosx$

Solve $dxdy =2x+3y+4x+2y+3 $

The solution of the differential equation $dx(x+2y_{3})dy =y$ is

Tangent to a curve intercepts the y-axis at a point $P$ A line perpendicular to this tangent through $P$ passes through another point $(1,0).$ The differential equation of the curve is

Find the differential equation of all parabolas whose axis are parallel to the x-axis.

Let $y(x)$ be a solution of the differential equation $(1+e_{x})y_{prime}+ye_{x}=1.$ If $y(0)=2$ , then which of the following statements is (are) true? (a)$y(−4)=0$ (b)$y(−2)=0$ (c)$y(x)$ has a critical point in the interval $(−1,0)$ (d)$y(x)$ has no critical point in the interval$(−1,0)$

The solution of differential equation $dxy(2x_{4}+y)dy =(1−4xy_{2})x_{2}$ is given by

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