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Question Number 130087 by bobhans last updated on 22/Jan/21

$$\frac{dx}{dy}=a+\frac{(b-a)y}{c}+\frac{(b-a)\sin \left(\frac{2\pi y}{c}\right)}{2\pi }$$ $$fora>0,b>0,c>0onx⩾0$$

Answered by benjo_mathlover last updated on 22/Jan/21

$$\mathrm{dx}=\mathrm{a}\mathrm{dy}+\frac{(\mathrm{b}-\mathrm{a})}{\mathrm{c}}\mathrm{y}\mathrm{dy}+\frac{\mathrm{b}-\mathrm{a}}{2\pi }\sin \left(\frac{2\pi \mathrm{y}}{\mathrm{c}}\right)\mathrm{dy}$$ $$\mathrm{x}=\mathrm{ay}+\frac{(\mathrm{b}-\mathrm{a}){\mathrm{y}}^2}{2\mathrm{c}}-\frac{(\mathrm{b}-\mathrm{a})\mathrm{c}}{4{\pi }^2}\cos \left(\frac{2\pi \mathrm{y}}{\mathrm{c}}\right)+\lambda$$

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