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Question Number 102639 by bobhans last updated on 10/Jul/20

$$\frac{dy}{dx}-2xy=6y{e}^{y^2}$$

Answered by Ar Brandon last updated on 10/Jul/20

$$\mathrm{Let}\mathrm{y}=\mathrm{vx}\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{v}+\mathrm{x}\frac{\mathrm{dv}}{\mathrm{dx}}$$$$\Rightarrow \mathrm{v}+\mathrm{x}\frac{\mathrm{dv}}{\mathrm{dx}}-{2\mathrm{vx}}^2={6\mathrm{vxe}}^{{\mathrm{v}}^2{\mathrm{x}}^2}$$$$\Rightarrow \mathrm{x}\frac{\mathrm{dv}}{\mathrm{dx}}=\mathrm{v}({6\mathrm{xe}}^{{\mathrm{v}}^2{\mathrm{x}}^2}+{2\mathrm{x}}^2-1)$$$$$$$$Anyideatoproceed?AmIontherighttrack?$$

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