First slide

Methods of solving first order first degree differential equations

Question

$The general solution of the differential equation y (5 x^{4} y + 1) dx + (x + 2 y + 2 x^{5} y) dy = 0 i s$

Moderate

A

${xy}^{2} {+x}^{5} {+y}^{2} =c$
B

${xy+x}^{5} y^{2} {+y}^{2} =c$
C

${xy+x}^{5} y^{2} +y=c$
D

${xy+x}^{5} {y+y}^{2} =c$

Solution

$\begin{array}{l} x d y + y d x + 5 x^{4} y^{2} d x + 2 x^{5} y d y + 2 y d y = 0 \\ \to d (xy) + d (x^{5} y^{2}) + d (y^{2}) = 0 \\ Integrating \\ \to x y + x^{5} y^{2} + y^{2} = c \end{array}$

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