A linear first order differential equation is of the first degree in the dependent variable and its derivative. dy The general form of a first order differential equation linear in y is dx + P(x)y = Q(x) where P and Q are functions of x only. Consider dx + P(x)y = Q(x), then its solution is yel P(x)dx = S Q(x) eS P(x)dx dx + C. dx Also, + G(y)x = H(y), where G and H are functions of y only, is a first order differential equation dy linear in x and has a solution equal to xel G(y)dy = § H (y) eS G()dydy + C %3D sin x Using linear first order differential equation, solve for the general solution of+ = cos x dy y Please dx show complete solutions.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.