Class 12

Math

Calculus

Differential Equations

Show that the given differential equation is homogeneous and solve each of them.$(x_{2}−y_{2})dx+2xydy=0$

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In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?

The general solution of the differential equation $yydx−xdy =0$is(A) $xy=C$ (B) $x=Cy_{2}$ (C) $y=Cx$ (D) $y=Cx_{2}$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=x_{2}+2x+C$ : $yprime−2x−2=0$

The general solution of the differential equation $e_{x}dy+(ye_{x}+2x)dx=0$is(A) $xe_{y}+x_{2}=C$ (B) $xe_{y}+y_{2}=C$ (C) $ye_{x}+x_{2}=C$ (D) $ye_{y}+x_{2}=C$

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

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

Find the equation of a curve passing through the point $(2,3)$, given that the slope of the tangent to the curve at any point (x, y) is $y_{2}2x $.

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