Please solve it anyone

1.	Please solve it anyone
Answer» GIVEN :– • Diffrential EQUATION – $\\ \implies \bf(1 + x^2) \dfrac{dy}{dx} + 2xy = cosx \\$ TO FIND :– • Solution of diffrential equation = ? SOLUTION :– $\\ \implies \bf(1 + x^2) \dfrac{dy}{dx} + 2xy = cosx \\$ $\\ \implies \bf\dfrac{dy}{dx} + \dfrac{2x}{(1 + x^2)}y = \dfrac{cosx}{(1 + x^2)} \\$ • COMPARE with – $\\ \implies \bf\dfrac{dy}{dx} +Py = Q \\$ • So – $\\ \implies \bf P =\dfrac{2x}{(1 + x^2)} \: \: and \: \: Q = \dfrac{cosx}{(1 + x^2)} \\$ • We know that – $\\ \implies \bf I.F. = e^{\int P.dx} \\$ $\\ \implies \bf I.F. = e^{\int \frac{2x}{(1 + x^2)}dx} \\$ $\\ \implies \bf I.F. = e^{ \log{(1 + x^2)}} \\$ $\\ \implies \large{ \boxed{\bf I.F. = 1 + {x}^{2} }}\\$ • Solution :– $\\ \implies \bf y(I.F.) = \int(I.F)Q.dx + c\\$ $\\ \implies \bf y(1 + {x}^{2} ) = \int\dfrac{cosx}{(1 + x^2)} \times (1 + {x}^{2}) .dx + c\\$ $\\ \implies \bf y(1 + {x}^{2} ) = \int\cos(x) .dx + c\\$ $\\ \implies \large { \boxed{\bf y(1 + {x}^{2} ) = \sin(x) + c}}\\$ is it CORRECT?

Answer»

• Diffrential EQUATION –

$\\ \implies \bf(1 + x^2) \dfrac{dy}{dx} + 2xy = cosx \\$