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Solve-the-equation-0-x-x-t-t-2-y-t-1-3-dt-1-2-0-x-5x-6t-y-t-dt-2x-0-




Question Number 137971 by EnterUsername last updated on 08/Apr/21
Solve the equation:  ∫_0 ^x (x−t)t^2 ((y(t)))^(1/3) dt+(1/2)∫_0 ^x (5x−6t)y(t)dt+2x=0
$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{x}−\mathrm{t}\right)\mathrm{t}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\mathrm{y}\left(\mathrm{t}\right)}\mathrm{dt}+\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{5x}−\mathrm{6t}\right)\mathrm{y}\left(\mathrm{t}\right)\mathrm{dt}+\mathrm{2x}=\mathrm{0} \\ $$

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