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In Exercises $1-10,$ find the general solution to the exact differential equation.$$\frac{d y}{d x}=5^{x} \ln 5+\frac{1}{x^{2}+1}$$

$$y=5^{x}+\tan ^{-1} x+C$$

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 6

Differential Equations and Mathematical Modeling

Section 1

Slope Fields and Euler's Method

Differentiation

Integration Techniques

Differential Equations

Second-Order Differential Equations

Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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this question asked us to find the general solution to the exact differential equation we know have been given D Y over DX. What we're going to do is we're going to put D y on the left hand side and then put our function times D acts on the right hand side. Okay, Now we can integrate both sides, and we have Why is five to the axe over Natural log of five times natural of a five. This is just gonna cancel when you multiply and divide by the same thing it cancels plus inverse tangent of acts. This is the formula for inverse tension of acts and then plus C Therefore, this simplifies toe Why is five to the axe plus inverse tangent of acts and then, plus our constant seeks we integrated

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