⧼exchistory⧽
7 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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[/math]
Find the general solution of each of the following differential equations.
- [a [math]\dydx = x^3 + 2e^x[/math]
- [math]x\dydx = 6x^3 +5x +1[/math]
- [math]\dydx = (y^2+1)(2x+3)[/math]
- [math]\dydx = xy + x[/math]
- [math]2xy^2 + \dydx - 4x^3y^2 = 0[/math]
- [math]y\dydx = \ln x[/math]
- [math]x\dydx = \ln x[/math]
- [math]\dydx + 16y = 0[/math]
- [math]\deriv2y + 16y = 0[/math]
- [math]\deriv2y = 16y[/math]
- [math]y^{\prime\prime} - 19y^{\prime} - 20y = 0[/math]
- [math](D^2 + 10D + 16)y = 0[/math]
- [math]2\deriv2y - 14\dydx = -20y[/math]
- [math]\deriv2y + a^2y = 2a\dydx[/math]
- [math](D^2 + 4D + 29)y = 0[/math]
- [math](y+5)\dydx = 7x - e^{-x}[/math]
- [math]\dydx = \frac xy[/math]
- [math]\dydx = \frac yx[/math]
- [math]\dydx = -\frac xy[/math]
- [math]\frac1y \deriv2y = 49[/math]
- [math](3x+4)\;dt + (4t+3)\;dx = 0[/math]
- [math]\dydx = \cot y[/math]
- [math]\frac1t \nxder{}yt = e^{3t^2+4}[/math]
- [math]\dydx = 3 \sin^2 x \cos^2 x[/math]
- [math]\dydx = 3 \sin^2 x \cos^2 y[/math]
- [math]\deriv2y = 6x^2 - 4x + 2[/math].
BBy Bot
Nov 03'24
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[/math]
Find the particular solution of each of the following differential equations which satisfies the given conditions.
- [math]\dydx = 3y[/math], \quad [math]y=5[/math] when [math]x=0[/math].
- [math]\deriv2y = 12x^2+1[/math], \quad graph passes through the point [math](1,-1)[/math] with a slope of [math]3[/math].
- [math]y\dydx = -x[/math], \quad graph passes through the point [math](-3,-4)[/math].
- [math]\nxder2st = -g \mbox{constant}[/math], \quad when [math]t=0[/math], [math]\nxder{}st = v_0[/math] and [math]s=s_0[/math].
- [math](D^2-2D-3)y = 0[/math], \quad [math]y=7[/math] and [math]\dydx = 1[/math] when [math]x=0[/math].
- [math](D^2-4D+13)y = 0[/math], \quad graph passes through [math](0,5)[/math] with a slope of [math]2[/math].
- [math](x+2)\dydx = 1[/math], \quad [math]y=\ln 9[/math] when [math]x=1[/math].
- [math](D^2-12D+36)y=0[/math], \quad [math]y=3[/math] and [math]\dydx=7[/math] when [math]x=0[/math].
BBy Bot
Nov 03'24
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[/math]
- lab{11.1.3a} Sketch the graph of [math]y=e^{\frac x2} \cos \left(x+\frac\pi4\right)[/math].
- Find a second-order, linear, homogeneous differential equation with constant coefficients of which the function in \ref{ex11.1.3a} is a solution.
BBy Bot
Nov 03'24
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[/math]
- lab{11.1.4a} Find the general solution of the differential equation [math](4D^2+8D+5)y = 0[/math].
- lab{11.1.4b} Find the particular solution of the differential equation in \ref{ex11.1.4a} whose graph passes through the point [math]\left(0, \frac{\sqrt2}2\right)[/math] with a slope of [math]-\frac{3\sqrt2}4[/math].
- Sketch the graph of the function in \ref{ex11.1.4b}.
BBy Bot
Nov 03'24
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[/math]
- lab{11.1.5a} Find the general solution of the differential equation [math](4D^2-8D+5)y = 0[/math].
- lab{11.1.5b} Find the particular solution of the differential equation in \ref{ex11.1.5a} whose graph passes through the point [math]\left(0, \frac{\sqrt2}2\right)[/math] with a slope of [math]\frac{\sqrt2}4[/math].
- Sketch the graph of the function in \ref{ex11.1.5b}.
BBy Bot
Nov 03'24
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[/math]
- lab{11.1.6a} Find the general solution of the differential equation [math](D^2+\frac14)y = 0[/math].
- lab{11.1.6b} Find the particular solution of the differential equation in \ref{ex11.1.6a} whose graph passes through the point [math]\left(0, \frac{\sqrt2}2\right)[/math] with a slope of [math]-\frac{\sqrt2}4[/math].
- Sketch the graph of the function in \ref{ex11.1.6b}.
BBy Bot
Nov 03'24
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[/math]
Find the general solution of the differential equation [math](D^2-2\alpha D +\alpha^2 + 1)y=0[/math], and sketch the graph for
- [math]\alpha \gt 0[/math]
- [math]\alpha = 0[/math]
- [math]\alpha \lt 0[/math].