Question

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

Answer 1

Answer on Question #69641 – Math – Differential Equations

Question

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

Solution

$$\begin{array}{l} dy = dx(e^{x} + x + \sin x) \\ \int dy = \int dx(e^{x} + x + \sin x) + C \\ y = e^{x} + \frac{x^{2}}{2} - \cos x + C \\ \end{array}$$

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

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