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Chapter 6: Q. 20 (page 575)

$\frac{d y}{d x} = 3 - 4 y, y (0) = 2$

Short Answer

Expert verified

The solution is $y (x) = \frac{1}{4} [3 + 5 e^{- 4 x}]$

Step by step solution

01

Step 1. Given information

given differential equation is $\frac{d y}{d x} = 3 - 4 y$

02

Step 2. solve equation

$鈭� \frac{1}{3 - 4 y} d y = 鈭� d x - \frac{1}{4} \ln (|3 - 4 y|) = x + c 1 \ln (|3 - 4 y|) = - 4 x - 4 c 1 3 - 4 y = A e^{- 4 x} y = \frac{1}{4} (3 - A e^{- 4 x}) 2 = \frac{1}{4} (3 - A) 8 - 3 = - A A = - 5 y (x) = \frac{1}{4} (3 + 5 e^{- 4 x})$

03

Step 3. The solution

The Solution is $y (x) = \frac{1}{4} [3 + 5 e^{- 4 x}]$

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