class 12

Math

Calculus

Differential Equations

Let $f:R→R$be a differentiable function with $f(0)=0$. If $y=f(x)$satisfies the differential equation $dxdy =(2+5x)(5x−2)1 $, then the value of $(lim)_{x→∞}f(x)$is ______

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Determine order and degree (if defined) of differential equations given$(dx_{2}d_{2}y )_{2}+cos(dxdy )=0$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$xy=gy+C$ : $yprime=1−xyy_{2} (xy=1)$

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

In a bank, principal increases continuously at the rate of 5% per year. An amountof Rs 1000 is deposited with this bank, how much will it worth after 10 years$(e_{0.5}=1.648)$

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

Find the general solution of the differential equations $(e_{x}+e_{−x})dy−(e_{x}−e_{−x})dx=0$

Find the general solution of the differential equations:$(x+y)dydx =1$

Form the differential equation of the family of hyperbola having foci on x-axis and center at the origin.