Find the solution to the differential equation $\frac { d y } { d x } = \frac { 6 x } { y }$ passing through $( 1,6 )$ .
A) $y ^ { 2 } = 6 x ^ { 2 } + 30$
B) $6 y ^ { 2 } = x ^ { 2 } + 215$
C) $y ^ { 2 } + 6 x ^ { 2 } = 42$
D) $6 y ^ { 2 } + x ^ { 2 } = 217$

Question

Quizplus · Accepted Answer

To solve the differential equation $\frac { d y } { d x } = \frac { 6 x } { y }$, we separate variables and integrate both sides: $\int y dy = \int 6x dx$, leading to $\frac{y^2}{2} = 3x^2 + C$. Using the initial condition $(1,6)$, we find $C = 30 - 3 = 27$, so the solution is $y^2 = 6x^2 + 54$, which simplifies to $y^2 = 6x^2 + 30$, matching option A.

Find the Solution to the Differential Equation dydx=6xy\frac { d y } { d x } = \frac { 6 x } { y }dxdy​=y6x​

Find the Solution to the Differential Equation $\frac { d y } { d x } = \frac { 6 x } { y }$