Find the general solution of the differential equation. $\frac { \mathrm { d } y } { \mathrm {~d} x } = 12 x y$
Solve for y as a function of x.

A) $y = C e ^ { x ^ { 2 } } + 6$
B) $y = C e ^ { 6 x ^ { 2 } }$
C) $y = C e ^ { 12 x }$
D) $y = C e ^ { 6 x }$
E) $y = e ^ { 6 x ^ { 2 } } + C$

Question

Find the general solution of the differential equation.   $\frac { \mathrm { d } y } { \mathrm {~d} x } = 12 x y$  
Solve for y as a function of x.
 
A) $y = C e ^ { x ^ { 2 } } + 6$
B)   $y = C e ^ { 6 x ^ { 2 } }$
C)   $y = C e ^ { 12 x }$
D)   $y = C e ^ { 6 x }$
E)   $y = e ^ { 6 x ^ { 2 } } + C$

Quizplus · Accepted Answer

This differential equation can be solved using separation of variables. Rearranging gives $\frac{1}{y} dy = 12x dx$. Integrating both sides, we get $\ln|y| = 6x^2 + C$, where $C$ is the constant of integration. Exponentiating both sides gives $y = Ce^{6x^2}$, which matches choice B.

Find the General Solution of the Differential Equation dy dx=12xy\frac { \mathrm { d } y } { \mathrm {~d} x } = 12 x y dxdy​=12xy

Find the General Solution of the Differential Equation $\frac { \mathrm { d } y } { \mathrm {~d} x } = 12 x y$