Class 12

Math

Calculus

Differential Equations

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$(e_{0.5}=1.648)$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

If $y=y(x)$ and it follows the relation $4xe_{xy}=y+5sin_{2}x,$ then $y_{prime}(0)$ is equal to______

Integrating factor of differential equation $cosxdxdy +ysinx=1$ is

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order

The force of resistance encountered by water on a motor boat of mass $m$ going in still water with velocity $v$ is proportional to the velocity $v˙$ At $t=0$ when its velocity is $v_{0},$ then engine shuts off. Find an expression for the position of motor boat at time $t$ and also the distance travelled by the boat before it comes to rest. Take the proportionality constant as $k>0.$

If the solution of the differential equation $dxdy −y=1−e_{−x}$ and $y(0)=y_{0}$ has a finite value, when $x→∞,$ then the value of $∣∣ y_{0}2 ∣∣ $ is__

The solution of the equation $(x_{2}y+x_{2})dx+y_{2}(x−1)dy=0$ is given by

A normal is drawn at a point $P(x,y)$ of a curve. It meets the x-axis at $Q˙$ If $PQ$ has constant length $k,$ then show that the differential equation describing such curves is $ydxdy =±k_{2}−y_{2} $ . Find the equation of such a curve passing through $(0,k)˙$

The general solution of the differential equation, $y_{prime}+yϕ_{prime}(x)−ϕ(x)ϕ_{prime}(x)=0$ , where $ϕ(x)$ is a known function, is