If frac{dy}{dx} + 2x tan(x-y) = 1,then sin(x- | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given differential equation is $\frac{dy}{dx} + 2x 	an(x-y) = 1$.Let $x-y = t$.Then $1 - \frac{dy}{dx} = \frac{dt}{dx}$,which implies $\frac{dy}{

Vedclass · Accepted Answer

$A e^{x^2}$

Vedclass · Answer

(C) Given differential equation is $\frac{dy}{dx} + 2x 	an(x-y) = 1$.Let $x-y = t$.Then $1 - \frac{dy}{dx} = \frac{dt}{dx}$,which implies $\frac{dy}{dx} = 1 - \frac{dt}{dx}$.Substituting this into the original equation:$1 - \frac{dt}{dx} + 2x 	an(t) = 1$.This simplifies to $\frac{dt}{dx} = 2x 	an(t)$,or $\frac{dt}{	an(t)} = 2x dx$.Integrating both sides: $\int \cot(t) dt = \int 2x dx$.$\ln|\sin(t)| = x^2 + C$.Let $C = \ln|A|$,so $\ln|\sin(t)| = x^2 + \ln|A|$.$\ln|\frac{\sin(t)}{A}| = x^2$.$\sin(t) = A e^{x^2}$.Substituting $t = x-y$ back,we get $\sin(x-y) = A e^{x^2}$.

If $\frac{dy}{dx} + 2x \tan(x-y) = 1$,then $\sin(x-y)$ is equal to

Similar Questions

The number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{5})^{256}$ is

Two spherical black bodies have radii $r_1$ and $r_2$. Their surface temperatures are $T_1$ and $T_2$. If they radiate the same power,then $\frac{r_2}{r_1}$ is:

Hydrated $AlCl_3$ is used as:

If a slab of insulating material $4 \times 10^{-3} \ m$ thick is introduced between the plates of a parallel plate capacitor,the separation between plates has to be increased by $3.5 \times 10^{-3} \ m$ to restore the capacity to its original value. The dielectric constant of the material will be

The total charge induced in a conducting loop when it is moved in a magnetic field depends on

Vedclass Test Series

Exam Paper Generator

Online Exam Module