It is given that $\left( 2xy\frac{\mathrm{d}y}{\mathrm{d}x}+{{y}^{2}} \right)\cos x=\frac{1}{x{{y}^{

Question

It is given that $\left( 2xy\frac{\mathrm{d}y}{\mathrm{d}x}+{{y}^{2}} \right)\cos x=\frac{1}{x{{y}^{2}}}$, where $0 Using the substitution $u=x{{y}^{2}}$, show that the differential equation can be reduced to $\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{\sec x}{u}$. [3] Hence find the general solution to the differential equation. [3]

Accepted Answer

(a) $\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\sec x}{u}$ (b) $x^2y^4=2\ln(\sec x+\tan x)+C$

2025 HCI P1 Q3

2025 HCI P1 Q3

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