Find the general solution of the differential equation. $\frac { \mathrm { d } y } { \mathrm {~d} x } = 27 x ^ { 2 } + 12 \sqrt { x }$
Solve for y as a function of x.

NOTE: Use the symbol C to enter the constant.

A) $y = 27 x ^ { 3 } + 8 x ^ { 1.5 } + C$
B) $y = 27 x ^ { 2 } + 8 x + C$
C) $y = 9 x ^ { 3 } + 8 x ^ { 1.5 } + C$
D) $y = 9 x - 8 x ^ { - 0.5 } + C$
E) $y = 27 x ^ { 3 } + 4 x ^ { 1.5 } + C$

Question

Find the general solution of the differential equation.   $\frac { \mathrm { d } y } { \mathrm {~d} x } = 27 x ^ { 2 } + 12 \sqrt { x }$  
Solve for y as a function of x.
 
NOTE: Use the symbol C to enter the constant.
 
A) $y = 27 x ^ { 3 } + 8 x ^ { 1.5 } + C$
B)   $y = 27 x ^ { 2 } + 8 x + C$
C)   $y = 9 x ^ { 3 } + 8 x ^ { 1.5 } + C$
D)   $y = 9 x - 8 x ^ { - 0.5 } + C$
E)   $y = 27 x ^ { 3 } + 4 x ^ { 1.5 } + C$

Quizplus · Accepted Answer

The general solution is found by integrating the given differential equation. Integrating $27x^2$ gives $9x^3$ and integrating $12\sqrt{x}$ gives $8x^{1.5}$. Thus, the solution is $y = 9x^3 + 8x^{1.5} + C$.

Find the General Solution of the Differential Equation dy dx=27x2+12x\frac { \mathrm { d } y } { \mathrm {~d} x } = 27 x ^ { 2 } + 12 \sqrt { x } dxdy​=27x2+12x​

Find the General Solution of the Differential Equation $\frac { \mathrm { d } y } { \mathrm {~d} x } = 27 x ^ { 2 } + 12 \sqrt { x }$