Question

Choose the correct option from the given alternatives:

The solution of ${\displaystyle \frac{\text{dy}}{\text{dx}}+\text{y}=\cos \text{x}-\sin \text{x}}$

Options

• ye^x = cos x + c

• ye^x + e^x  cos x = c

• ye^x = e^x cos x + c

• y²e^x = e^x cos x + c

Answer 1

ye^x = e^x cos x + c

Hint:

${\displaystyle \frac{\text{dy}}{\text{dx}}+\text{y}=\cos \text{x}-\sin \text{x}}$

I.F. = ${\displaystyle {\text{e}}^{\int 1\text{dx}}={\text{e}}^{\text{x}}}$

∴ the solution is ${\displaystyle \text{y}\cdot {\text{e}}^{\text{x}}=\int (\cos \text{x}-\sin \text{x}){\text{e}}^{\text{x}}+\text{c}}$ 

∴ ye^x = e^x cos x + c