91Ó°ÊÓ

Find the indicated particular solutions of the given differential equations. \(y^{\prime} \sqrt{x}+\frac{1}{2} y=e^{\sqrt{x}} ; \quad x=1\) when \(y=3\)

Find the particular solutions of the given differential equations that satisfy the given conditions. $$9 D^{2} y+16 y=0 ; \quad D y=0 \text { and } y=2 \text { when } x=\pi / 2$$

Find the particular solution of each differential equation for the given conditions. $$3 y^{\prime \prime}-10 y^{\prime}+3 y=x e^{-2 x} ; \quad y^{\prime}=-\frac{9}{35} \text { and } y=-\frac{13}{35} \text { when } x=0$$

Solve the given differential equations. $$y \sqrt{1-x^{2}} d y+2 d x=0$$

Solve the given problems by solving the appropriate differential equation. If a circuit contains only an inductance and a resistance, with \(L=2.0 \mathrm{H}\) and \(\bar{R}=30 \Omega,\) find the current \(i\) as a function of time \(t\) if \(i=0.020 \mathrm{A}\) when \(t=0 .\) See Fig. 31.9.

Solve the given third-and fourth-order differential equations. $$D^{4} y-D^{3} y-9 D^{2} y+9 D y=0$$

Find the indicated particular solutions of the given differential equations. \((\sin x) y^{\prime}+y=\tan x ; \quad x=\pi / 4\) when \(y=0\)

Find the particular solutions of the given differential equations that satisfy the given conditions. $$D^{2} y+16 y=8 D y ; \quad D y=2 \text { and } y=4 \text { when } x=0$$

Find the particular solution of each differential equation for the given conditions. $$y^{\prime \prime}+y=x+\sin 2 x ; \quad y^{\prime}=1 \text { and } y=0 \text { when } x=\pi$$

Find the particular solution of the given differential equation for the indicated values. $$\frac{d y}{d x}+y x^{2}=0 ; \quad x=0 \text { when } y=1$$