Class 12

Math

Calculus

Differential Equations

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 $.

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A function y=f(x) satisfies the differential equation dydx−y=cosx−sinx with initial condition that y is bounded when x→∞. The area enclosed by y=f(x),y=cosx and the y-axis is

Solve $[x e_{−2x} −x y ]dydx =1(x=0)$

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

If y=y(x) and 2+sinx1+y(dydx)=−cosx,y(0)=1,then y(π2) equals

Which of the following is not the differential equation of family of curves whose tangent form an angle of $4π $ with the hyperbola $xy=c_{2}$? \displaystyle{\left({a}\right)}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=\frac{{{x}-{y}}}{{{x}+{y}}}{\left({b}\right)}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=\frac{{{x}}}{{{x}-{y}}}{\left({c}\right)}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=\frac{{{x}+{y}}}{{{x}-{y}}} (d)N.O.T.

The form of the differential equation of the central conics $ax_{2}+by_{2}=1$ is

Find the equation of the curve in which the subnormal varies as the square of the ordinate.

The differential equation(1+y2)xdx−(1+x2)ydy=0 Represents a family of: