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