WGU D204 OBJECTIVE ASSESSMENT AND PA LATEST 2025 TEST BANK

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MATH 3321 EMath Final Exam |

Questions and Answers | 2026 Update |

100% Correct - UH.

1. The general solution of the differential

equation dydx=2xdxdy=2x is:

A) y=x2+Cy=x2+C

B) y=2x2+Cy=2x2+C

C) y=x2y=x2

D) y=2x+Cy=2x+C

Answer: A

Rationale: Integrate both

sides: ∫dy=∫2xdx∫dy=∫2xdx → y=x2+Cy=x2+C. This is the

general solution.

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Q2. Which of the following is a separable ODE?

A) dydx=x+ydxdy=x+y

B) dydx=xydxdy=yx

C) dydx=xydxdy=xy

D) Both B and C

Answer: D

Rationale: Separable equations can be written

as g(y)dy=h(x)dxg(y)dy=h(x)dx. Option B: ydy=xdxydy=xdx;

Option C: 1ydy=xdxy1dy=xdx. Option A is not separable.




Q3. Solve the initial value problem: dydx=3ydxdy

=3y, y(0)=2y(0)=2.

A) y=2e3xy=2e3x

B) y=3e2xy=3e2x

C) y=e3x+1y=e3x+1

D) y=2exy=2ex

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Answer: A

Rationale: Separate: dyy=3dxydy=3dx.

Integrate: ln⁡∣y∣=3x+Cln∣y∣=3x+C.

Exponentiate: y=Ce3xy=Ce3x. Use y(0)=2y(0)=2 → C=2C=2.

So y=2e3xy=2e3x.




Q4. The integrating factor for the linear ODE dydx+2y=exdxdy

+2y=ex is:

A) e2xe2x

B) e−2xe−2x

C) exex

D) e−xe−x

Answer: A

Rationale: For y′+P(x)y=Q(x)y′+P(x)y=Q(x), integrating

factor μ=e∫Pdx=e∫2dx=e2xμ=e∫Pdx=e∫2dx=e2x.

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Q5. (Scenario) A tank initially contains 100 L of pure water.

Brine with 0.2 kg/L salt flows in at 5 L/min, and the well-mixed

solution flows out at 5 L/min. The salt amount S(t)S(t) satisfies:

A) dSdt=1−0.05SdtdS=1−0.05S

B) dSdt=0.2−0.05SdtdS=0.2−0.05S

C) dSdt=1−0.2SdtdS=1−0.2S

D) dSdt=0.2+0.05SdtdS=0.2+0.05S

Answer: A

Rationale: Rate in = (5 L/min)(0.2 kg/L) = 1 kg/min. Rate out =

(S/100)*5 = 0.05S kg/min. So dSdt=1−0.05SdtdS=1−0.05S.




Q6. The equation dydx=2xydxdy=y2x is:

A) Linear

B) Separable