The image displays a page from an examination paper from the Ladoke Akintola University of Technology, Ogbomosho, Nigeria. The document is titled "DEPARTMENT OF PURE AND APPLIED MATHEMATICS" and the course is "Elementary Differential Equations (MTH202)". The session is "2025/2026 Academic Session" and the time allowed is "50 minutes". The instructions state to "Answer All Questions carefully". There are two questions presented on the page. Question One is a differential equation: $(x^2 - 9) \frac{dy}{dx} + xy = 0$. It has two parts: a. Find the general solution to the differential equation. b. State the Existence and Uniqueness theorem. c. Verify that the differential equation below is exact and hence solve. Question Two is also a differential equation with initial conditions: $y''(x) - y'(x) - 6y(x) = e^{-2x}$. It has three parts: a. Use variation of parameters method to solve. b. Using Laplace transform method, solve $y''(x) - y'(x) - 6y(x) = e^{-2x}$, $y(0)=0$, $y'(0)=1$, $y''(0)=2$. c. Differentiate between Ordinary and Partial Differential Equations. The page also includes "Best Wishes!". The lighting suggests the image was taken indoors with natural light, possibly from a window. The paper appears to be slightly creased. in Ogbomosho, Nigeria

$The image displays a page from an examination paper from the Ladoke Akintola University of Technology, Ogbomosho, Nigeria. The document is titled "DEPARTMENT OF PURE AND APPLIED MATHEMATICS" and the course is "Elementary Differential Equations (MTH202)". The session is "2025/2026 Academic Session" and the time allowed is "50 minutes". The instructions state to "Answer All Questions carefully". There are two questions presented on the page. Question One is a differential equation: $(x^2 - 9) \frac{dy}{dx} + xy = 0$. It has two parts: a. Find the general solution to the differential equation. b. State the Existence and Uniqueness theorem. c. Verify that the differential equation below is exact and hence solve. Question Two is also a differential equation with initial conditions: $y''(x) - y'(x) - 6y(x) = e^{-2x}$. It has three parts: a. Use variation of parameters method to solve. b. Using Laplace transform method, solve $y''(x) - y'(x) - 6y(x) = e^{-2x}$, $y(0)=0$, $y'(0)=1$, $y''(0)=2$. c. Differentiate between Ordinary and Partial Differential Equations. The page also includes "Best Wishes!". The lighting suggests the image was taken indoors with natural light, possibly from a window. The paper appears to be slightly creased.$

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Jun 19, 2026

Ogbomosho, Nigeria

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The image displays a page from an examination paper from the Ladoke Akintola University of Technology, Ogbomosho, Nigeria. The document is titled "DEPARTMENT OF PURE AND APPLIED MATHEMATICS" and the course is "Elementary Differential Equations (MTH202)". The session is "2025/2026 Academic Session" and the time allowed is "50 minutes". The instructions state to "Answer All Questions carefully". There are two questions presented on the page. Question One is a differential equation: $(x^2 - 9) \frac{dy}{dx} + xy = 0$. It has two parts: a. Find the general solution to the differential equation. b. State the Existence and Uniqueness theorem. c. Verify that the differential equation below is exact and hence solve. Question Two is also a differential equation with initial conditions: $y''(x) - y'(x) - 6y(x) = e^{-2x}$. It has three parts: a. Use variation of parameters method to solve. b. Using Laplace transform method, solve $y''(x) - y'(x) - 6y(x) = e^{-2x}$, $y(0)=0$, $y'(0)=1$, $y''(0)=2$. c. Differentiate between Ordinary and Partial Differential Equations. The page also includes "Best Wishes!". The lighting suggests the image was taken indoors with natural light, possibly from a window. The paper appears to be slightly creased.

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