Class 12

Math

Calculus

Differential Equations

Find the general solution of the differential equations $x_{5}dxdy =−y_{5}$

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The function $y=f(x)$ is the solution of the differential equation $dxdy +x_{2}−1xy =1−x_{2} x_{4}+2x $ in $(−1,1)$ satisfying $f(0)=0.$ Then $∫_{23}f(x)dx$ is

Show that the differential equation $y_{3}dy+(x+y_{2})dx=0$ can be reduced to a homogeneous equation.

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

Find the order and degree of the following differential equation: $ln(dxdy )=ax+by$

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

Solve the equation $dxdy =2y1ny+y−xy $

Solve $dxg(dy) =4x−2y−2$ , given that $y=1$ when $x=1.$

The differential equation of all non-horizontal lines in a plane is