Question 46 of 96intermediate🔧 ApplyMCQ1 mark

The general solution of the differential equation dydx=ex+y\frac{dy}{dx} = e^{x+y} is

Exercise: EXERCISE 9.3 | Q: 23 | (Page 13)
For More Understanding

Explanation

The question asks for the general solution of a separable differential equation. Following the method shown in Example 20 of the textbook context, we separate variables and integrate both sides. The solution matches option (A).

Solution Steps

  1. Step 1: Rewrite the differential equation by separating the exponential term: dy/dx = e^(x+y) = exe^{x} · eye^{y}

  2. Step 2: Separate the variables: e^(-y) dy = exe^{x} dx

  3. Step 3: Integrate both sides: ∫e^(-y) dy = ∫exe^{x} dx

  4. Step 4: Apply integration: -e^(-y) = exe^{x} + C

  5. Step 5: Rearrange to get the general solution: exe^{x} + e^(-y) = C

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