Final Answer
Step-by-step Solution
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Combine all terms into a single fraction with $\sqrt{x^2+1}$ as common denominator
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$e^{-x}+\frac{dy}{dx}=\frac{1+6x\sqrt{x^2+1}}{\sqrt{x^2+1}}$
Learn how to solve problems step by step online. Solve the differential equation e^(-x)+dy/dx=1/((x^2+1)^1/2)+6x. Combine all terms into a single fraction with \sqrt{x^2+1} as common denominator. Rearrange terms. Multiplying the fraction by -1. We need to isolate the dependent variable , we can do that by simultaneously subtracting \frac{-1-6x\sqrt{x^2+1}}{\sqrt{x^2+1}} from both sides of the equation.