Class 12

Math

Calculus

Differential Equations

Prove that $x_{2}−y_{2}=c(x_{2}+y_{2})_{2}$is the general solution of differential equation $(x_{3}−2xy_{2})dx=(y_{3}−3x_{2}y)dy$, where c is a parameter.

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Form the differential equation representing the family of ellipses having foci on x-axis and centre at the origin.

Show that the given differential equation is homogeneous and solve each of them.$x_{2}dxdy =x_{2}−2y_{2}+xy$

Find the general solution of the differential equations:$dydx +2y=sinx$

Find a particular solution of the differential equation $(x+1)dxdy =2e_{−y}−1$given that $y=0$when$x=0$.

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

Find the particular solution of the differential equation $dxdy +ycotx=2x+x_{2}cotx(x=0)$given that $y=0$when $x=2π $.

The differential equations , find the particular solution satisfying the given condition:$dxdy −xy +cosec(xy )=0;y=0$when x = 1