Question

Solve the general solution of dy/dx=e^x+x+sinx

Answer 1

Answer to Question #89355 – Math – Differential Equations

Question

1. Solve the general solution of $\frac{dy}{dx} = e^x + x + \sin x$

Solution

Given,

$$\frac{dy}{dx} = e^x + x + \sin x$$

Integrating with respect to $x$ , we get

$$y(x) = \int (e^x + x + \sin x) dx + C,$$

where $C$ is an integration constant;

$$y(x) = e^x + \frac{x^2}{2} - \cos x + C \text{ is the required general solution.}$$

Answer: $y(x) = e^x + \frac{x^2}{2} - \cos x + C$ .

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