Solve the differential equation.
-$$3 x ^ { 2 } y ^ { \prime } - 2 x y = y ^ { - 3 }$$
A) $y ^ { 4 } = \frac { - 4 } { 11 x } + C x ^ { 8 / 3 }$
B) $y ^ { 4 } = \frac { - 4 } { 11 x } + C x ^ { 11 / 3 }$
C) $y ^ { 2 } = \frac { - 4 } { 11 x } + C x ^ { 11 / 3 }$
D) $y ^ { 2 } = \frac { - 4 } { 11 x } + C x ^ { 8 / 3 }$

Question

Quizplus · Accepted Answer

This differential equation can be solved by first rewriting it in a form that allows separation of variables or by recognizing it as a first-order linear differential equation in the form $x^2y' - 2xy = y^{-3}$. Multiplying through by $y^3$ gives $x^2y'y^3 - 2xy^4 = 1$, which can be recognized as a derivative of a product after rearranging, leading to an integration that ultimately results in the solution $y^4 = \frac{-4}{11x} + Cx^{8/3}$, where $C$ is the integration constant.

Solve the Differential Equation 3x2y′−2xy=y−33 x ^ { 2 } y ^ { \prime } - 2 x y = y ^ { - 3 }3x2y′−2xy=y−3

Solve the Differential Equation $3 x ^ { 2 } y ^ { \prime } - 2 x y = y ^ { - 3 }$