Category: Differential Equation

Question Number 130301 by sarahvalencia last updated on 24/Jan/21 Answered by benjo_mathlover last updated on 24/Jan/21 $$\left(2\right)\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\mathrm{x}}^2}{{\mathrm{y}}^2}\Rightarrow \int {\mathrm{y}}^2\mathrm{dy}-\int {\mathrm{x}}^2\mathrm{dx}=\mathrm{C}$$$$\:\mathrm{y}^{\mathrm{3}} −\mathrm{x}^{\mathrm{3}} \:=\:\mathrm{3C}\:;\:\mathrm{y}^{\mathrm{3}}…

Question Number 129949 by bemath last updated on 21/Jan/21 $$\mathrm{Given}8\sqrt{\mathrm{x}}\left(\sqrt{9+\sqrt{\mathrm{x}}}\right)\mathrm{dy}=\frac{\mathrm{dx}}{\sqrt{4+\sqrt{9+\sqrt{\mathrm{x}}}}},\mathrm{x}>1$$$$\mathrm{and}\mathrm{y}\left(0\right)=\sqrt{7}.\mathrm{Find}\mathrm{y}\left(256\right).$$ Answered by liberty last updated on 21/Jan/21 $$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{8\sqrt{\mathrm{x}}\left(\sqrt{9+\sqrt{\mathrm{x}}}\right)\left(\sqrt{4+\sqrt{9+\sqrt{\mathrm{x}}}}\right)}$$$$\:\mathrm{let}\:\sqrt{\mathrm{4}+\sqrt{\mathrm{9}+\sqrt{\mathrm{x}}}\:}\:=\:\mathrm{z}\:;\:\sqrt{\mathrm{9}+\sqrt{\mathrm{x}}}\:=\:\mathrm{z}^{\mathrm{2}} −\mathrm{4}…

Question Number 129777 by stelor last updated on 18/Jan/21 $$(x^2-xy-y^2)dx+x^{2}dy=0$$$$hello\dots pleasehelpme.$$ Answered by Ar Brandon last updated on 18/Jan/21…

Question Number 129656 by Ahmed1hamouda last updated on 17/Jan/21 Commented by Ahmed1hamouda last updated on 17/Jan/21 $$solvethedifferen\mathrm{tial}\mathrm{equation}$$ Answered by liberty last updated on…

Question Number 129334 by bramlexs22 last updated on 15/Jan/21 $$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}+{\mathrm{y}}^3\cos \mathrm{x}$$ Answered by liberty last updated on 15/Jan/21 $$\mathrm{let}\mathrm{y}={\mathrm{w}}^{-\frac{1}{2}}\to \frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2}{\mathrm{w}}^{-3/2}\frac{\mathrm{dw}}{\mathrm{dx}}$$$$\:\Rightarrow−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{xw}^{−\mathrm{3}/\mathrm{2}}…