If the equation of the curve which passes thr | vedclass

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

Question

(D) Given the differential equation: $\frac{dy}{dx} = \frac{2x-5y+3}{5x+2y-3}$ Rearranging the terms: $(5x+2y-3)dy = (2x-5y+3)dx$ $(5x+2y-3)dy - (2x-5

Vedclass · Accepted Answer

$x^2-5xy-y^2+3x+3y-1=0$

Vedclass · Answer

(D) Given the differential equation: $\frac{dy}{dx} = \frac{2x-5y+3}{5x+2y-3}$ Rearranging the terms: $(5x+2y-3)dy = (2x-5y+3)dx$ $(5x+2y-3)dy - (2x-5y+3)dx = 0$ $5x dy + 2y dy - 3 dy - 2x dx + 5y dx - 3 dx = 0$ Group the terms: $5(x dy + y dx) + (2y dy - 2x dx) - (3 dy + 3 dx) = 0$ This can be written as: $5 d(xy) + d(y^2) - d(x^2) - 3 d(x+y) = 0$ Integrating both sides: $5xy + y^2 - x^2 - 3(x+y) = C$ Since the curve passes through $(1,1)$, substitute $x=1$ and $y=1$: $5(1)(1) + (1)^2 - (1)^2 - 3(1+1) = C$ $5 + 1 - 1 - 6 = C \Rightarrow C = -1$ Substituting $C$ back into the equation: $5xy + y^2 - x^2 - 3x - 3y = -1$ Rearranging: $x^2 - 5xy - y^2 + 3x + 3y - 1 = 0$ Thus, the correct option is $D$.

If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{dy}{dx} = \frac{2x-5y+3}{5x+2y-3}$, then the equation of that curve is:

Similar Questions

$A$ curve passes through the point $(3,2)$ for which the segment of the tangent line contained between the coordinate axes is bisected at the point of contact. The equation of the curve is

If a curve passes through the origin,such that the length of the subnormal is equal to one more than the square of the ordinate,then:

If the population grows at the rate of $8 \%$ per year,then the time taken for the population to be doubled is $\quad$ (given $\log 2=0.6912$ ) (in $years$)

In a bank,the principal increases continuously at a rate of $x \%$ per year. Then the rate,$x$,if ₹$100$ doubles itself in $10$ years,is (Given $\log 2 = 0.6931$) (in $\%$)

In a bank,the principal increases continuously at the rate of $r \%$ per year. Find the value of $r$ if $Rs \, 100$ doubles itself in $10$ years $\left(\log _{e} 2=0.6931\right)$. (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module