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In Exercises $1-10,$ find the general solution to…
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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70

Problem 3 Medium Difficulty

In Exercises $1-10,$ find the general solution to the exact differential equation.
$$\frac{d y}{d x}=\sin x-e^{-x}+8 x^{3}$$

Answer

$$
y=-\cos x+e^{-x}+2 x^{4}+C
$$

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3
Calculus; Graphical, Numerical, Algebraic

Chapter 6

Differential Equations and Mathematical Modeling

Section 1

Slope Fields and Euler's Method

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Integration Techniques

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Video Transcript

this question asked us to find the general solution to the exact differential equation. What we know we have is d Y over DX. We're just gonna write D Y in the left hand side and then write the function on the right hand side. You have the DX on the right hand side now take the integral of both sides and we can differentiate or we can integrate. Why is negative coastline of acts? Because the integral sign is Kasan negative coastline minus negative. Eat the negative axe. Plus we can use the power rule increased the exported by one divide by the new exponents And then we can simplify this negative co sign acts plus each the negative acts negative negative is positive, plus two extra the fourth pussy.

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Ross L. Finney, Franklin D. Demana, Bet K. Waits, Daniel Kennedy

Calculus; Graphical, Numerical, Algebraic

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Related Topics

Differentiation

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