Question

What is the general solution of the differential y'= y/(x+1)

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Dexter

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54 Answers

Given differential equation is: \frac{dy}{dx} = \frac{y}{x+1} .

Step 1: Separate the variables:

\frac{dy}{y} = \frac{dx}{x+1}

Step 2: Integrate both sides:

\int\frac{1}{y} dy = \int\frac{1}{x+1} dx

Step 3: Solve the integrals:

ln|y| = ln|x+1| + C

Step 4: Eliminate the natural logarithms:

e^{ln|y|} = e^{ln|x+1| + C}

Step 5: Simplify the equation:

y = e^C \cdot |x + 1|

Step 6: Finally, rewrite the arbitrary constant ase^C = C_1 :

\boxed{y = C_1 \cdot |x + 1|} , where C_1 is an arbitrary constant.

Step 1: Separate the variables:

Step 2: Integrate both sides:

Step 3: Solve the integrals:

Step 4: Eliminate the natural logarithms:

Step 5: Simplify the equation:

Step 6: Finally, rewrite the arbitrary constant as

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