Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 127578 by bramlexs22 last updated on 31/Dec/20

$$\mathrm{y}{}^{″}=5\mathrm{y}-{10\mathrm{y}}^2$$$$\mathrm{y}\left(0\right)=1$$

Answered by mr W last updated on 31/Dec/20

$$y^{″}=\frac{{dy}^{\prime }}{dx}=y^{\prime }\frac{{dy}^{\prime }}{dy}$$$$y^{\prime }\frac{{dy}^{\prime }}{dy}=5y-10y^2$$$$\frac{1}{2}{\left(y^{\prime }\right)}^2=\frac{5y^2}{2}-\frac{10y^3}{3}+\frac{C_1}{2}$$$$y^{\prime }=\frac{dy}{dx}=\pm \sqrt{5y^2-\frac{20y^3}{3}+C_1}$$$$\pm \frac{dy}{\sqrt{5y^2-\frac{20y^3}{3}+C_1}}=dx$$$$x=\pm \int \frac{dy}{\sqrt{5y^2-\frac{20y^3}{3}+C_1}}$$$$......$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com