$\text { Find the general solution of the differential equation } \frac { d y } { d x } = \frac { 5 x ^ { 2 } } { 8 y ^ { 2 } } \text {. }$
A) $y = \frac { 5 } { 8 } x ^ { 3 } + C ^ { \prime }$
B) $y = \sqrt [ 3 ] { \frac { 5 } { 8 } x ^ { 3 } + C }$
C) $y = \sqrt { \frac { 8 } { 5 } x ^ { 3 } + C }$
D) $y = \sqrt [ 3 ] { \frac { x ^ { 2 } } { 8 } + C }$
E) $y = \sqrt [ 3 ] { 5 x ^ { 3 } + 8 C }$

Question

Quizplus · Accepted Answer

To solve the differential equation $\frac{dy}{dx} = \frac{5x^2}{8y^2}$, we separate variables and integrate both sides: $\int y^2 dy = \int \frac{5}{8} x^2 dx$, leading to $\frac{1}{3}y^3 = \frac{5}{24}x^3 + C$, which simplifies to $y^3 = \frac{5}{8}x^3 + C'$. Taking the cube root of both sides gives $y = \sqrt[3]{\frac{5}{8}x^3 + C}$.

Find the general solution of the differential equation dydx=5x28y2. \text { Find the general solution of the differential equation } \frac { d y } { d x } = \frac { 5 x ^ { 2 } } { 8 y ^ { 2 } } \text {. } Find the general solution of the differential equation dxdy​=8y25x2​.

$\text { Find the general solution of the differential equation } \frac { d y } { d x } = \frac { 5 x ^ { 2 } } { 8 y ^ { 2 } } \text {. }$