Differential Equations
Separable — Conic Solution
nta_pyq_2024_apr
Grade 12
Question:
The solution curve of the differential equation $2y\dfrac{dy}{dx}+3=5\dfrac{dy}{dx}$, passing through the point $(0,1)$ is a conic, whose vertex lies on the line:
$2x+3y=9$
$2x+3y=-9$
$2x+3y=-6$
$2x+3y=6$
Step-by-Step Solution
Key Concept: $(2y-5)dy=-3dx$. Integrate: $y^2-5y=-3x+C$. Through $(0,1)$: $C=-4$. Rewrite: $(y-5/2)^2=-3(x-3/4)$, parabola with vertex $(3/4,5/2)$.
Vertex $(3/4,5/2)$ lies on $2x+3y=9$.
Correct Answer: 1