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Question Number 92708 by Rio Michael last updated on 08/May/20

$$\mathrm{solve}\mathrm{the}\mathrm{differential}\mathrm{equations}.$$$$\left(\mathrm{a}\right)(x+3y^2)\frac{d^{2}y}{{dx}^2}+6y{\left(\frac{dy}{dx}\right)}^2+2\frac{dy}{dx}+2=0$$$$\left(\mathrm{b}\right)(2y-x)\frac{d^{2}y}{{dx}^2}+2{\left(\frac{dy}{dx}\right)}^2-2\frac{dy}{dx}+2=0$$

Answered by peter frank last updated on 09/May/20

$$letp=y^{{}^{\prime }}$$$$\frac{dp}{dx}=y^{″}$$$$(x+3y^2)\frac{d^{2}y}{{dx}^2}+6y{\left(\frac{dy}{dx}\right)}^2+2\frac{dy}{dx}+2=0$$$$(x+3y^2)\frac{dp}{dx}+6y{\left(p\right)}^2+2p+2=0$$$$(x+3y^2)\frac{dp}{dx}+6y{\left(p\right)}^2+2p+2=0$$$$\frac{dp}{dx}=\frac{dp}{dy}.\frac{dy}{dx}=\frac{dp}{dy}.p$$$$(x+3y^2)\frac{dp}{dx}.p+6y{\left(p\right)}^2+2p+2=0$$$$........$$$$$$$$$$

Commented by Rio Michael last updated on 10/May/20

$$\mathrm{okay}\mathrm{bro}\mathrm{thats}\mathrm{great}$$

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