Solve the initial value problem.
-$$\frac { d y } { d x } = 3 x ^ { - 3 / 4 } , y ( 1 ) = 8$$
A) $y = 12 x ^ { 1 / 4 } + 96$
B) $y = 12 x ^ { 1 / 4 } - 4$
C) $y = 3 x ^ { 1 / 4 } + 5$
D) $y = - \frac { 3 } { 4 } x ^ { - 7 / 4 } - 1$

Question

Quizplus · Accepted Answer

We can integrate both sides with respect to $x$ to obtain $y = 4x^{1/4} + C$. Using the initial condition $y(1) = 8$, we get $C = 4$ and hence $y = 4x^{1/4} + 4 = 12x^{1/4} - 4$. Therefore, the correct choice is (B).

Solve the Initial Value Problem dydx=3x−3/4,y(1)=8\frac { d y } { d x } = 3 x ^ { - 3 / 4 } , y ( 1 ) = 8dxdy​=3x−3/4,y(1)=8

Solve the Initial Value Problem $\frac { d y } { d x } = 3 x ^ { - 3 / 4 } , y ( 1 ) = 8$