class 12

Math

Calculus

Differential Equations

A curve passes through the point $(1,6π )$ . Let the slope of the curve at each point $(x,y)$ be $xy +sec(xy ),x>0.$ Then the equation of the curve is

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The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4

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

The general solution of a differential equation of the type $dydx +P_{1}x=Q_{1}$is(A) $ye_{∫P_{1}dy}=∫(Q_{1}e_{∫P_{1}dy})dy+C$ (B) $ye˙_{∫P_{1}dx}=∫(Q_{1}e_{∫P_{1}dx})dx+C$(C) $xe_{∫P_{1}dy}=∫(Q_{1}e_{∫P_{1}dy})dy+C$ (D) $xe_{∫p_{1}dx}=∫Q_{1}e_{∫p_{1}dx}dx+C$

Find the general solution of the differential equations y log y dx – x dy = 0

Which of the following differential equations has $y=c_{1}e_{x}+c_{2}e_{−x}$as the general solution?(A) $dx_{2}d_{2}y +y=0$ (B) $dx_{2}d_{2}y −y=0$ (C) $dx_{2}d_{2}y +1=0$ (D) $dx_{2}d_{2}y −1=0$

Find a particular solution of the differential equation $dydx +ycotx=1(x=0)4xcosecx$$(x=0)$, given that $y=0$when $x=2π $

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

Form the differential equation of the family of circles touching the y-axis at origin.