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Chapter 6: Q. 19 (page 575)

$\frac{d y}{d x} = 5 y, y (0) = 1$

Short Answer

Expert verified

The solution is $y (x) = e^{5 x}$

Step by step solution

Step 1. Given information

Given differential equation is $\frac{d y}{d x} = 5 y, y (0) = 1$

Step 2. Solve the equation

$\frac{d y}{d x} = 5 y, y (0) = 1 \int \frac{1}{y} d y = \int 5 d x \ln (|y|) = 5 x + c y = e^{5 x + c} = A e^{5 x + c} A = 1 y (x) = e^{5 x}$

Step 3. The solution

The solution is $y (x) = e^{5 x}$

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Most popular questions from this chapter

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dydx=5y,y0=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the equation

Step 3. The solution

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$\frac{d y}{d x} = 5 y, y (0) = 1$