Category: Differential Equation

Question Number 119567 by abdul88 last updated on 25/Oct/20 $$$$$$(1-x)\frac{d^{2}y}{{dx}^2}+x\frac{dy}{dx}-xy=\frac{1}{1-x},x\ne 1$$$$haspowerseriessolutionfor\mid x\mid <1$$ Answered by mathmax by abdo last updated…

Question Number 119472 by Engr_Jidda last updated on 24/Oct/20 Answered by Sach last updated on 24/Oct/20 $$\{\begin{array}{l}{y}^{″}+{xy}^{\prime }-y=x^2+1\\ y\left(0\right)=1\\ y^{\prime }\left(0\right)=2\end{array}$$$$1^{\mathrm{rst}}\mathrm{step}:{let}^{\prime }ssuposethereissuchasolutionandthatitisaserie$$$$(sorryforthespelling{I}^{\prime }mfrenchsoIhopeyouunderstandwhatIwrightandthatIdidnotmisunderstandyourquestion$$$${let}'{s}\:{call}\:\left({a}_{{k}}…

Question Number 184937 by MikeH last updated on 14/Jan/23 $$\mathrm{find}\mathrm{the}\mathrm{laplace}\mathrm{transform}\mathrm{of}\mathrm{the}\mathrm{differential}$$$$\mathrm{equation}\mathrm{below}$$$$\frac{dy}{dt}+5y\left(t\right)+6{\int }_0^{t}y\left(\tau \right)d\tau =u\left(t\right)\mathrm{where}y\left(0\right)=2$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 119290 by bobhans last updated on 23/Oct/20 $$(3x-y+1)dx+(6x+2y-3)dy=0$$ Answered by TANMAY PANACEA last updated on 23/Oct/20 $$dy(6x+2y-3)=(-3x+y-1)dx$$$$\frac{dy}{dx}=\frac{-3x+y-1}{6x+2y-3}$$$${x}={X}+{h}…

Question Number 119233 by bemath last updated on 23/Oct/20 $$(D^2-5D+6)y=e^{3x}$$ Answered by benjo_mathlover last updated on 23/Oct/20 $$(D-2I)(D-3I)\left(y\right)=e^{3x};I\left(y\right)=y$$$${let}\:\left({D}−\mathrm{3}{I}\right)\left({y}\right)\:=\:{z} \…