Final Answer
Step-by-step Solution
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Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$
Learn how to solve differential equations problems step by step online.
$\sqrt{x}\frac{dy}{dx}=e^ye^{\left(\sqrt{x}\right)}$
Learn how to solve differential equations problems step by step online. Solve the differential equation x^1/2dy/dx=e^(y+x^1/2). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to . Solve the integral \int\frac{1}{e^y}dy and replace the result in the differential equation.