class 12

Math

Calculus

Differential Equations

If $y(x)$ satisfies the differential equation $y_{prime}−ytanx=2xsecx$ and $y(0)=0$ , then

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

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

The general solution of the differential equation $dxdy =e_{x+y}$is(A) $e_{x}+e_{−y}=C$ (B) $e_{x}+e_{y}=C$(C) $e_{−x}+e_{y}=C$ (D) $e_{−x}+e_{−y}=C$

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point $(4,3)$. Find the equation of the curve given that it passes through $(2,1)$.

Find a particular solution of the differential equation$(x−y)(dx+dy)=dxdy$, given that $y=1$, when $x=0$. (Hint: put $x−y=t$).

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: $y=xsinx$ : $xyprime=y+xx_{2}−y_{2} (x=0$and$x>yorx<y$)

The differential equations, find a particular solution satisfying the given condition: $x(x_{2}−1)dxdy =1;y=0$when $x=2$

Find the general solution of the differential equations:$(1+x_{2})dy+2xydx=cotxdx(x=0)$