Category: Differential Equation

Question Number 96217 by john santu last updated on 30/May/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}=\left(\frac{{\mathrm{y}}^2-{\mathrm{x}}^2+\mathrm{y}}{\mathrm{x}}\right)$$ Answered by bobhans last updated on 30/May/20 $$\mathrm{set}\mathrm{y}=xz\Rightarrow \frac{dy}{dx}=z+x\frac{dz}{dx}$$$${z}\:+\:{x}\:\frac{{dz}}{{dx}}\:=\:\frac{{x}^{\mathrm{2}}…

Question Number 96125 by john santu last updated on 30/May/20 $${4\mathrm{x}}^2{\mathrm{y}}^{″}+{12\mathrm{xy}}^{\prime }+3\mathrm{y}=0$$ Answered by john santu last updated on 30/May/20 $$\mathrm{cauchy}-\mathrm{euler}$$$$\mathrm{4r}^{\mathrm{2}}…

Question Number 96065 by john santu last updated on 29/May/20 $${\mathrm{y}}^{\prime }+\mathrm{y}=\mathrm{x}\sqrt[3]{{\mathrm{y}}^2}$$ Answered by bobhans last updated on 29/May/20 $$\mathrm{Bernoulli}\mathrm{eq}$$$$\mathrm{v}\:=\:\mathrm{y}^{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{3}}} \:=\:\mathrm{y}^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 95933 by john santu last updated on 28/May/20 $${\mathrm{y}}^{‴}+{2\mathrm{y}}^{\prime }-3\mathrm{y}={\mathrm{e}}^{\mathrm{x}}(\mathrm{x}+3)$$ Commented by Sourav mridha last updated on 29/May/20 $$\mathrm{are}\mathrm{you}\mathrm{sure}\mathrm{it}\mathrm{is}3\mathrm{rd}\mathrm{order}\mathrm{ODE},\mathrm{i}\mathrm{think}$$$$\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{2nd}\:\mathrm{order}.…

Question Number 95748 by bobhans last updated on 27/May/20 $${\mathrm{y}}^{″}=\sin \mathrm{x}-\cos \mathrm{x}$$ Answered by mathmax by abdo last updated on 27/May/20 $$\Rightarrow {\mathrm{y}}^{{}^{\prime }}=\int (\mathrm{sinx}-\mathrm{cosx})\mathrm{dx}=-\mathrm{cosx}-\mathrm{sinx}+\mathrm{c}\Rightarrow \mathrm{y}=\int (-\mathrm{cosx}-\mathrm{sinx}+\mathrm{c})\mathrm{dx}$$$$−\mathrm{sinx}\:+\mathrm{cosx}\:+\mathrm{cx}\:+\lambda…