Home / AP Calculus BC : 7.6 Finding General Solutions Using Separation of Variables- Exam Style questions with Answer- MCQ

AP Calculus BC : 7.6 Finding General Solutions Using Separation of Variables- Exam Style questions with Answer- MCQ

Question

The temperature of a solid at time t ≥ 0 is modeled by the nonconstant function H and increases according to the differential equation \(\frac{dH}{dt}=2H+1\) , where H(t)  is measured in degrees Fahrenheit and t is measured in hours. Which of the following must be true?

A \(H=H^2+ t + C\)

B \(ln |2H+1| = t/2 + C\)

C \(ln |2H+1| = t + C\)

D \(ln |2H+1| = 2t + C\)

Answer/Explanation

 

Question

At each point (x , y )  on a certain curve, the slope of the curve is \(3x^{2} y \). If the curve contains the point ( 0,8)  , then its equation is

(A)\(y=8e^{x^{3}}\)                 (B)\(y=x^{3}+8\)                        (C)\(y=e^{x^{3}}+7\)                (D)\(y=In(x+1)+8\)                  (E)\(y^{2}=x^{3}+8\)

Answer/Explanation

 

Question 

 The general solution of the differential equation \(y’=y+x^{2} \)is y=

(A)\(Ce^{x}\)                       (B)\(Ce^{x}+x^{2}\)                  (C)\(-x^{2}-2x-2+C (D)e^{x}-x^{2}-2x-2+C\)                               (E)\(Ce^{x}-x^{2}-2x-2\)

Answer/Explanation

Ans:E

 

Question

 The general solution for the equation \(\frac{dy}{dx}+y=xe^{-x}\) is

(A)\(y=\frac{x^{2}}{2}e^{-x}+Ce^{-x}\)
(B)\(y=\frac{x^{2}}{2}e^{-x}+e^{-x}+C\)
(C)\(y=-e^{-x}+\frac{C}{1+x}\)
(D)\(xe^{-x}+Ce^{-x}\)
(E)\(C_{1}e^{-x}+C_{2}xe^{-x}\)

Answer/Explanation

Ans:A

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