Solve the differential equation. $\frac { d P } { d x } = 15 x ^ { 4 } - 5 , \quad P ( - 2 ) = 8$
A) $P ( x ) = 3 x ^ { 5 } + 5 x$
B) $P ( x ) = 3 x ^ { 5 } + 94$
C) $P ( x ) = 3 x ^ { 5 } - 5 x + 94$
D) $P ( x ) = 60 x ^ { 3 } - 5 x + 94$
E) $P ( x ) = 3 x ^ { 5 } + C$

Question

Solve the differential equation. $\frac { d P } { d x } = 15 x ^ { 4 } - 5 , \quad P ( - 2 ) = 8$ 
A) $P ( x ) = 3 x ^ { 5 } + 5 x$
B) $P ( x ) = 3 x ^ { 5 } + 94$
C) $P ( x ) = 3 x ^ { 5 } - 5 x + 94$
D) $P ( x ) = 60 x ^ { 3 } - 5 x + 94$
E) $P ( x ) = 3 x ^ { 5 } + C$

Quizplus · Accepted Answer

Integrating both sides gives us $P(x) = 3x^5 - 5x + C$. Plugging in $P(-2) = 8$ gives us $C=94$, so our solution is $P(x) = 3x^5 - 5x + 94$. Therefore, the answer is choice (C).

Solve the Differential Equation dPdx=15x4−5,P(−2)=8\frac { d P } { d x } = 15 x ^ { 4 } - 5 , \quad P ( - 2 ) = 8dxdP​=15x4−5,P(−2)=8

Solve the Differential Equation $\frac { d P } { d x } = 15 x ^ { 4 } - 5 , \quad P ( - 2 ) = 8$